Differential geometry applied to dynamical systems /:
This book aims to present a new approach called flow curvature method that applies differential geometry to dynamical systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory -- or the flow -- may be an...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, N.J. :
World Scientific,
2009.
|
| Schriftenreihe: | World Scientific series on nonlinear science. Monographs and treatises ;
vol. 66. World Scientific series on nonlinear science. Monographs and treatises ; v. 66. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book aims to present a new approach called flow curvature method that applies differential geometry to dynamical systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory -- or the flow -- may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence ... |
| Beschreibung: | 1 online resource (xxvii, 312 pages :) |
| Bibliographie: | Includes bibliographical references (pages 297-307) and index. |
| ISBN: | 9789814277150 9814277150 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn593212992 | ||
| 003 | OCoLC | ||
| 005 | 20240705115654.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 100402s2009 njua ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e pn |c N$T |d MERUC |d YDXCP |d OSU |d EBLCP |d COCUF |d E7B |d IDEBK |d OCLCQ |d FVL |d OCLCQ |d UIU |d OCLCQ |d DEBSZ |d OCLCQ |d NLGGC |d OCLCQ |d OCLCO |d OCLCQ |d OCLCF |d OCLCQ |d LOA |d AZK |d OCLCQ |d AGLDB |d MOR |d PIFAG |d ZCU |d OCLCQ |d JBG |d OCLCQ |d U3W |d STF |d WRM |d OCLCQ |d VTS |d ICG |d INT |d NRAMU |d VT2 |d AU@ |d OCLCQ |d WYU |d REC |d OCLCQ |d DKC |d OCLCQ |d M8D |d UKAHL |d OCLCQ |d UKCRE |d UIU |d OCLCO |d S2H |d OCLCO |d OCLCQ |d OCLCO |d OCLCQ |d OCLCL | ||
| 019 | |a 536309763 |a 614872597 |a 647853226 |a 669248803 |a 712987411 |a 722736530 |a 728058859 |a 960205191 |a 961487816 |a 962622059 |a 988518851 |a 991948174 |a 1037937181 |a 1038660835 |a 1045530917 |a 1064201190 |a 1081273792 |a 1153527891 |a 1228600965 |a 1289522829 | ||
| 020 | |a 9789814277150 |q (electronic bk.) | ||
| 020 | |a 9814277150 |q (electronic bk.) | ||
| 020 | |z 9789814277143 | ||
| 020 | |z 9814277142 | ||
| 035 | |a (OCoLC)593212992 |z (OCoLC)536309763 |z (OCoLC)614872597 |z (OCoLC)647853226 |z (OCoLC)669248803 |z (OCoLC)712987411 |z (OCoLC)722736530 |z (OCoLC)728058859 |z (OCoLC)960205191 |z (OCoLC)961487816 |z (OCoLC)962622059 |z (OCoLC)988518851 |z (OCoLC)991948174 |z (OCoLC)1037937181 |z (OCoLC)1038660835 |z (OCoLC)1045530917 |z (OCoLC)1064201190 |z (OCoLC)1081273792 |z (OCoLC)1153527891 |z (OCoLC)1228600965 |z (OCoLC)1289522829 | ||
| 050 | 4 | |a QA845 |b .G56 2009eb | |
| 072 | 7 | |a SCI |x 018000 |2 bisacsh | |
| 082 | 7 | |a 531.11 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Ginoux, Jean-Marc. |0 http://id.loc.gov/authorities/names/no2009112727 | |
| 245 | 1 | 0 | |a Differential geometry applied to dynamical systems / |c Jean-Marc Ginoux. |
| 260 | |a Hackensack, N.J. : |b World Scientific, |c 2009. | ||
| 300 | |a 1 online resource (xxvii, 312 pages :) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file |2 rda | ||
| 490 | 1 | |a World scientific series on nonlinear science. Series A. ; |v vol. 66 | |
| 504 | |a Includes bibliographical references (pages 297-307) and index. | ||
| 520 | |a This book aims to present a new approach called flow curvature method that applies differential geometry to dynamical systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory -- or the flow -- may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence ... | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Preface; Acknowledgments; Contents; List of Figures; List of Examples; Dynamical Systems; 1. Differential Equations; 1.1 Galileo's pendulum; 1.2 D'Alembert transformation; 1.3 From differential equations to dynamical systems; 2. Dynamical Systems; 2.1 State space -- phase space; 2.2 Definition; 2.3 Existence and uniqueness; 2.4 Flow, fixed points and null-clines; 2.5 Stability theorems; 2.5.1 Linearized system; 2.5.2 Hartman-Grobman linearization theorem; 2.5.3 Liapouno. stability theorem; 2.6 Phase portraits of dynamical systems; 2.6.1 Two-dimensional systems; 2.6.2 Three-dimensional systems. | |
| 505 | 8 | |a 2.7 Various types of dynamical systems2.7.1 Linear and nonlinear dynamical systems; 2.7.2 Homogeneous dynamical systems; 2.7.3 Polynomial dynamical systems; 2.7.4 Singularly perturbed systems; 2.7.5 Slow-Fast dynamical systems; 2.8 Two-dimensional dynamical systems; 2.8.1 Poincare index; 2.8.2 Poincare contact theory; 2.8.3 Poincare limit cycle; 2.8.4 Poincare-Bendixson Theorem; 2.9 High-dimensional dynamical systems; 2.9.1 Attractors; 2.9.2 Strange attractors; 2.9.3 First integrals and Lie derivative; 2.10 Hamiltonian and integrable systems; 2.10.1 Hamiltonian dynamical systems. | |
| 505 | 8 | |a 2.10.2 Integrable system2.10.3 K.A.M. Theorem; 3. Invariant Sets; 3.1 Manifold; 3.1.1 Definition; 3.1.2 Existence; 3.2 Invariant sets; 3.2.1 Global invariance; 3.2.2 Local invariance; 4. Local Bifurcations; 4.1 CenterManifold Theorem; 4.1.1 Center manifold theorem for flows; 4.1.2 Center manifold approximation; 4.1.3 Center manifold depending upon a parameter; 4.2 Normal FormTheorem.; 4.3 Local Bifurcations of Codimension 1; 4.3.1 Saddle-node bifurcation; 4.3.2 Transcritical bifurcation; 4.3.3 Pitchfork bifurcation; 4.3.4 Hopf bifurcation; 5. Slow-Fast Dynamical Systems; 5.1 Introduction. | |
| 505 | 8 | |a 5.2 Geometric Singular Perturbation Theory5.2.1 Assumptions; 5.2.2 Invariance; 5.2.3 Slow invariant manifold; 5.3 Slow-fast dynamical systems -- Singularly perturbed systems; 5.3.1 Singularly perturbed systems; 5.3.2 Slow-fast autonomous dynamical systems; 6. Integrability; 6.1 Integrability conditions, integrating factor, multiplier; 6.1.1 Two-dimensional dynamical systems; 6.1.2 Three-dimensional dynamical systems; 6.2 First integrals -- Jacobi's last multiplier theorem; 6.2.1 First integrals; 6.2.2 Jacobi's last multiplier theorem; 6.3 Darboux theory of integrability. | |
| 505 | 8 | |a 6.3.1 Algebraic particular integral -- General integral6.3.2 General integral; 6.3.3 Multiplier; 6.3.4 Algebraic particular integral and fixed points; 6.3.5 Homogeneous polynomial dynamical systems of degree m; 6.3.6 Homogeneous polynomial dynamical systems of degree two; 6.3.7 Planar polynomial dynamical systems; Differential Geometry; 7. Differential Geometry; 7.1 Concept of curves -- Kinematics vector functions; 7.1.1 Trajectory curve; 7.1.2 Instantaneous velocity vector; 7.1.3 Instantaneous acceleration vector; 7.2 Gram-Schmidt process -- Generalized Fr ́enet moving frame. | |
| 650 | 0 | |a Dynamics. |0 http://id.loc.gov/authorities/subjects/sh85040316 | |
| 650 | 0 | |a Geometry, Differential. |0 http://id.loc.gov/authorities/subjects/sh85054146 | |
| 650 | 6 | |a Dynamique. | |
| 650 | 6 | |a Géométrie différentielle. | |
| 650 | 7 | |a kinetics (dynamics) |2 aat | |
| 650 | 7 | |a SCIENCE |x Mechanics |x Dynamics. |2 bisacsh | |
| 650 | 7 | |a Dynamics |2 fast | |
| 650 | 7 | |a Geometry, Differential |2 fast | |
| 758 | |i has work: |a Differential geometry applied to dynamical systems (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFqrfKCtRg4KxWDFqG9KwK |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Ginoux, Jean-Marc. |t Differential geometry applied to dynamical systems. |d Hackensack, N.J. : World Scientific, 2009 |z 9789814277143 |w (OCoLC)311763235 |
| 830 | 0 | |a World Scientific series on nonlinear science. |n Series A, |p Monographs and treatises ; |v vol. 66. |0 http://id.loc.gov/authorities/names/no94008495 | |
| 830 | 0 | |a World Scientific series on nonlinear science. |n Series A, |p Monographs and treatises ; |v v. 66. |0 http://id.loc.gov/authorities/names/no94008495 | |
| 856 | 1 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305321 |3 Volltext | |
| 856 | 1 | |l CBO01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305321 |3 Volltext | |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH24686361 | ||
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL477153 | ||
| 938 | |a ebrary |b EBRY |n ebr10361897 | ||
| 938 | |a EBSCOhost |b EBSC |n 305321 | ||
| 938 | |a YBP Library Services |b YANK |n 3161757 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn593212992 |
|---|---|
| _version_ | 1813903356657139712 |
| adam_text | |
| any_adam_object | |
| author | Ginoux, Jean-Marc |
| author_GND | http://id.loc.gov/authorities/names/no2009112727 |
| author_facet | Ginoux, Jean-Marc |
| author_role | |
| author_sort | Ginoux, Jean-Marc |
| author_variant | j m g jmg |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA845 |
| callnumber-raw | QA845 .G56 2009eb |
| callnumber-search | QA845 .G56 2009eb |
| callnumber-sort | QA 3845 G56 42009EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Preface; Acknowledgments; Contents; List of Figures; List of Examples; Dynamical Systems; 1. Differential Equations; 1.1 Galileo's pendulum; 1.2 D'Alembert transformation; 1.3 From differential equations to dynamical systems; 2. Dynamical Systems; 2.1 State space -- phase space; 2.2 Definition; 2.3 Existence and uniqueness; 2.4 Flow, fixed points and null-clines; 2.5 Stability theorems; 2.5.1 Linearized system; 2.5.2 Hartman-Grobman linearization theorem; 2.5.3 Liapouno. stability theorem; 2.6 Phase portraits of dynamical systems; 2.6.1 Two-dimensional systems; 2.6.2 Three-dimensional systems. 2.7 Various types of dynamical systems2.7.1 Linear and nonlinear dynamical systems; 2.7.2 Homogeneous dynamical systems; 2.7.3 Polynomial dynamical systems; 2.7.4 Singularly perturbed systems; 2.7.5 Slow-Fast dynamical systems; 2.8 Two-dimensional dynamical systems; 2.8.1 Poincare index; 2.8.2 Poincare contact theory; 2.8.3 Poincare limit cycle; 2.8.4 Poincare-Bendixson Theorem; 2.9 High-dimensional dynamical systems; 2.9.1 Attractors; 2.9.2 Strange attractors; 2.9.3 First integrals and Lie derivative; 2.10 Hamiltonian and integrable systems; 2.10.1 Hamiltonian dynamical systems. 2.10.2 Integrable system2.10.3 K.A.M. Theorem; 3. Invariant Sets; 3.1 Manifold; 3.1.1 Definition; 3.1.2 Existence; 3.2 Invariant sets; 3.2.1 Global invariance; 3.2.2 Local invariance; 4. Local Bifurcations; 4.1 CenterManifold Theorem; 4.1.1 Center manifold theorem for flows; 4.1.2 Center manifold approximation; 4.1.3 Center manifold depending upon a parameter; 4.2 Normal FormTheorem.; 4.3 Local Bifurcations of Codimension 1; 4.3.1 Saddle-node bifurcation; 4.3.2 Transcritical bifurcation; 4.3.3 Pitchfork bifurcation; 4.3.4 Hopf bifurcation; 5. Slow-Fast Dynamical Systems; 5.1 Introduction. 5.2 Geometric Singular Perturbation Theory5.2.1 Assumptions; 5.2.2 Invariance; 5.2.3 Slow invariant manifold; 5.3 Slow-fast dynamical systems -- Singularly perturbed systems; 5.3.1 Singularly perturbed systems; 5.3.2 Slow-fast autonomous dynamical systems; 6. Integrability; 6.1 Integrability conditions, integrating factor, multiplier; 6.1.1 Two-dimensional dynamical systems; 6.1.2 Three-dimensional dynamical systems; 6.2 First integrals -- Jacobi's last multiplier theorem; 6.2.1 First integrals; 6.2.2 Jacobi's last multiplier theorem; 6.3 Darboux theory of integrability. 6.3.1 Algebraic particular integral -- General integral6.3.2 General integral; 6.3.3 Multiplier; 6.3.4 Algebraic particular integral and fixed points; 6.3.5 Homogeneous polynomial dynamical systems of degree m; 6.3.6 Homogeneous polynomial dynamical systems of degree two; 6.3.7 Planar polynomial dynamical systems; Differential Geometry; 7. Differential Geometry; 7.1 Concept of curves -- Kinematics vector functions; 7.1.1 Trajectory curve; 7.1.2 Instantaneous velocity vector; 7.1.3 Instantaneous acceleration vector; 7.2 Gram-Schmidt process -- Generalized Fr ́enet moving frame. |
| ctrlnum | (OCoLC)593212992 |
| dewey-full | 531.11 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531.11 |
| dewey-search | 531.11 |
| dewey-sort | 3531.11 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>07290cam a2200661 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn593212992</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20240705115654.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cnu---unuuu</controlfield><controlfield tag="008">100402s2009 njua ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">N$T</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">N$T</subfield><subfield code="d">MERUC</subfield><subfield code="d">YDXCP</subfield><subfield code="d">OSU</subfield><subfield code="d">EBLCP</subfield><subfield code="d">COCUF</subfield><subfield code="d">E7B</subfield><subfield code="d">IDEBK</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">FVL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UIU</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">NLGGC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">LOA</subfield><subfield code="d">AZK</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AGLDB</subfield><subfield code="d">MOR</subfield><subfield code="d">PIFAG</subfield><subfield code="d">ZCU</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">JBG</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">U3W</subfield><subfield code="d">STF</subfield><subfield code="d">WRM</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">ICG</subfield><subfield code="d">INT</subfield><subfield code="d">NRAMU</subfield><subfield code="d">VT2</subfield><subfield code="d">AU@</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">WYU</subfield><subfield code="d">REC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">DKC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">M8D</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UKCRE</subfield><subfield code="d">UIU</subfield><subfield code="d">OCLCO</subfield><subfield code="d">S2H</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCL</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">536309763</subfield><subfield code="a">614872597</subfield><subfield code="a">647853226</subfield><subfield code="a">669248803</subfield><subfield code="a">712987411</subfield><subfield code="a">722736530</subfield><subfield code="a">728058859</subfield><subfield code="a">960205191</subfield><subfield code="a">961487816</subfield><subfield code="a">962622059</subfield><subfield code="a">988518851</subfield><subfield code="a">991948174</subfield><subfield code="a">1037937181</subfield><subfield code="a">1038660835</subfield><subfield code="a">1045530917</subfield><subfield code="a">1064201190</subfield><subfield code="a">1081273792</subfield><subfield code="a">1153527891</subfield><subfield code="a">1228600965</subfield><subfield code="a">1289522829</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789814277150</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9814277150</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9789814277143</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9814277142</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)593212992</subfield><subfield code="z">(OCoLC)536309763</subfield><subfield code="z">(OCoLC)614872597</subfield><subfield code="z">(OCoLC)647853226</subfield><subfield code="z">(OCoLC)669248803</subfield><subfield code="z">(OCoLC)712987411</subfield><subfield code="z">(OCoLC)722736530</subfield><subfield code="z">(OCoLC)728058859</subfield><subfield code="z">(OCoLC)960205191</subfield><subfield code="z">(OCoLC)961487816</subfield><subfield code="z">(OCoLC)962622059</subfield><subfield code="z">(OCoLC)988518851</subfield><subfield code="z">(OCoLC)991948174</subfield><subfield code="z">(OCoLC)1037937181</subfield><subfield code="z">(OCoLC)1038660835</subfield><subfield code="z">(OCoLC)1045530917</subfield><subfield code="z">(OCoLC)1064201190</subfield><subfield code="z">(OCoLC)1081273792</subfield><subfield code="z">(OCoLC)1153527891</subfield><subfield code="z">(OCoLC)1228600965</subfield><subfield code="z">(OCoLC)1289522829</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA845</subfield><subfield code="b">.G56 2009eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">SCI</subfield><subfield code="x">018000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">531.11</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ginoux, Jean-Marc.</subfield><subfield code="0">http://id.loc.gov/authorities/names/no2009112727</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Differential geometry applied to dynamical systems /</subfield><subfield code="c">Jean-Marc Ginoux.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Hackensack, N.J. :</subfield><subfield code="b">World Scientific,</subfield><subfield code="c">2009.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xxvii, 312 pages :)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">data file</subfield><subfield code="2">rda</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">World scientific series on nonlinear science. Series A. ;</subfield><subfield code="v">vol. 66</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 297-307) and index.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book aims to present a new approach called flow curvature method that applies differential geometry to dynamical systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory -- or the flow -- may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence ...</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Preface; Acknowledgments; Contents; List of Figures; List of Examples; Dynamical Systems; 1. Differential Equations; 1.1 Galileo's pendulum; 1.2 D'Alembert transformation; 1.3 From differential equations to dynamical systems; 2. Dynamical Systems; 2.1 State space -- phase space; 2.2 Definition; 2.3 Existence and uniqueness; 2.4 Flow, fixed points and null-clines; 2.5 Stability theorems; 2.5.1 Linearized system; 2.5.2 Hartman-Grobman linearization theorem; 2.5.3 Liapouno. stability theorem; 2.6 Phase portraits of dynamical systems; 2.6.1 Two-dimensional systems; 2.6.2 Three-dimensional systems.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.7 Various types of dynamical systems2.7.1 Linear and nonlinear dynamical systems; 2.7.2 Homogeneous dynamical systems; 2.7.3 Polynomial dynamical systems; 2.7.4 Singularly perturbed systems; 2.7.5 Slow-Fast dynamical systems; 2.8 Two-dimensional dynamical systems; 2.8.1 Poincare index; 2.8.2 Poincare contact theory; 2.8.3 Poincare limit cycle; 2.8.4 Poincare-Bendixson Theorem; 2.9 High-dimensional dynamical systems; 2.9.1 Attractors; 2.9.2 Strange attractors; 2.9.3 First integrals and Lie derivative; 2.10 Hamiltonian and integrable systems; 2.10.1 Hamiltonian dynamical systems.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.10.2 Integrable system2.10.3 K.A.M. Theorem; 3. Invariant Sets; 3.1 Manifold; 3.1.1 Definition; 3.1.2 Existence; 3.2 Invariant sets; 3.2.1 Global invariance; 3.2.2 Local invariance; 4. Local Bifurcations; 4.1 CenterManifold Theorem; 4.1.1 Center manifold theorem for flows; 4.1.2 Center manifold approximation; 4.1.3 Center manifold depending upon a parameter; 4.2 Normal FormTheorem.; 4.3 Local Bifurcations of Codimension 1; 4.3.1 Saddle-node bifurcation; 4.3.2 Transcritical bifurcation; 4.3.3 Pitchfork bifurcation; 4.3.4 Hopf bifurcation; 5. Slow-Fast Dynamical Systems; 5.1 Introduction.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">5.2 Geometric Singular Perturbation Theory5.2.1 Assumptions; 5.2.2 Invariance; 5.2.3 Slow invariant manifold; 5.3 Slow-fast dynamical systems -- Singularly perturbed systems; 5.3.1 Singularly perturbed systems; 5.3.2 Slow-fast autonomous dynamical systems; 6. Integrability; 6.1 Integrability conditions, integrating factor, multiplier; 6.1.1 Two-dimensional dynamical systems; 6.1.2 Three-dimensional dynamical systems; 6.2 First integrals -- Jacobi's last multiplier theorem; 6.2.1 First integrals; 6.2.2 Jacobi's last multiplier theorem; 6.3 Darboux theory of integrability.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">6.3.1 Algebraic particular integral -- General integral6.3.2 General integral; 6.3.3 Multiplier; 6.3.4 Algebraic particular integral and fixed points; 6.3.5 Homogeneous polynomial dynamical systems of degree m; 6.3.6 Homogeneous polynomial dynamical systems of degree two; 6.3.7 Planar polynomial dynamical systems; Differential Geometry; 7. Differential Geometry; 7.1 Concept of curves -- Kinematics vector functions; 7.1.1 Trajectory curve; 7.1.2 Instantaneous velocity vector; 7.1.3 Instantaneous acceleration vector; 7.2 Gram-Schmidt process -- Generalized Fr ́enet moving frame.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Dynamics.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85040316</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Geometry, Differential.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85054146</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Dynamique.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Géométrie différentielle.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">kinetics (dynamics)</subfield><subfield code="2">aat</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">SCIENCE</subfield><subfield code="x">Mechanics</subfield><subfield code="x">Dynamics.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Dynamics</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Geometry, Differential</subfield><subfield code="2">fast</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Differential geometry applied to dynamical systems (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCFqrfKCtRg4KxWDFqG9KwK</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Ginoux, Jean-Marc.</subfield><subfield code="t">Differential geometry applied to dynamical systems.</subfield><subfield code="d">Hackensack, N.J. : World Scientific, 2009</subfield><subfield code="z">9789814277143</subfield><subfield code="w">(OCoLC)311763235</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">World Scientific series on nonlinear science.</subfield><subfield code="n">Series A,</subfield><subfield code="p">Monographs and treatises ;</subfield><subfield code="v">vol. 66.</subfield><subfield code="0">http://id.loc.gov/authorities/names/no94008495</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">World Scientific series on nonlinear science.</subfield><subfield code="n">Series A,</subfield><subfield code="p">Monographs and treatises ;</subfield><subfield code="v">v. 66.</subfield><subfield code="0">http://id.loc.gov/authorities/names/no94008495</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305321</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="1" ind2=" "><subfield code="l">CBO01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305321</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24686361</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest Ebook Central</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL477153</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10361897</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">305321</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">3161757</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn593212992 |
| illustrated | Illustrated |
| indexdate | 2024-10-25T16:17:23Z |
| institution | BVB |
| isbn | 9789814277150 9814277150 |
| language | English |
| oclc_num | 593212992 |
| open_access_boolean | |
| owner | MAIN |
| owner_facet | MAIN |
| physical | 1 online resource (xxvii, 312 pages :) |
| psigel | ZDB-4-EBA |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | World Scientific, |
| record_format | marc |
| series | World Scientific series on nonlinear science. Monographs and treatises ; |
| series2 | World scientific series on nonlinear science. Series A. ; |
| spelling | Ginoux, Jean-Marc. http://id.loc.gov/authorities/names/no2009112727 Differential geometry applied to dynamical systems / Jean-Marc Ginoux. Hackensack, N.J. : World Scientific, 2009. 1 online resource (xxvii, 312 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file rda World scientific series on nonlinear science. Series A. ; vol. 66 Includes bibliographical references (pages 297-307) and index. This book aims to present a new approach called flow curvature method that applies differential geometry to dynamical systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory -- or the flow -- may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence ... Print version record. Preface; Acknowledgments; Contents; List of Figures; List of Examples; Dynamical Systems; 1. Differential Equations; 1.1 Galileo's pendulum; 1.2 D'Alembert transformation; 1.3 From differential equations to dynamical systems; 2. Dynamical Systems; 2.1 State space -- phase space; 2.2 Definition; 2.3 Existence and uniqueness; 2.4 Flow, fixed points and null-clines; 2.5 Stability theorems; 2.5.1 Linearized system; 2.5.2 Hartman-Grobman linearization theorem; 2.5.3 Liapouno. stability theorem; 2.6 Phase portraits of dynamical systems; 2.6.1 Two-dimensional systems; 2.6.2 Three-dimensional systems. 2.7 Various types of dynamical systems2.7.1 Linear and nonlinear dynamical systems; 2.7.2 Homogeneous dynamical systems; 2.7.3 Polynomial dynamical systems; 2.7.4 Singularly perturbed systems; 2.7.5 Slow-Fast dynamical systems; 2.8 Two-dimensional dynamical systems; 2.8.1 Poincare index; 2.8.2 Poincare contact theory; 2.8.3 Poincare limit cycle; 2.8.4 Poincare-Bendixson Theorem; 2.9 High-dimensional dynamical systems; 2.9.1 Attractors; 2.9.2 Strange attractors; 2.9.3 First integrals and Lie derivative; 2.10 Hamiltonian and integrable systems; 2.10.1 Hamiltonian dynamical systems. 2.10.2 Integrable system2.10.3 K.A.M. Theorem; 3. Invariant Sets; 3.1 Manifold; 3.1.1 Definition; 3.1.2 Existence; 3.2 Invariant sets; 3.2.1 Global invariance; 3.2.2 Local invariance; 4. Local Bifurcations; 4.1 CenterManifold Theorem; 4.1.1 Center manifold theorem for flows; 4.1.2 Center manifold approximation; 4.1.3 Center manifold depending upon a parameter; 4.2 Normal FormTheorem.; 4.3 Local Bifurcations of Codimension 1; 4.3.1 Saddle-node bifurcation; 4.3.2 Transcritical bifurcation; 4.3.3 Pitchfork bifurcation; 4.3.4 Hopf bifurcation; 5. Slow-Fast Dynamical Systems; 5.1 Introduction. 5.2 Geometric Singular Perturbation Theory5.2.1 Assumptions; 5.2.2 Invariance; 5.2.3 Slow invariant manifold; 5.3 Slow-fast dynamical systems -- Singularly perturbed systems; 5.3.1 Singularly perturbed systems; 5.3.2 Slow-fast autonomous dynamical systems; 6. Integrability; 6.1 Integrability conditions, integrating factor, multiplier; 6.1.1 Two-dimensional dynamical systems; 6.1.2 Three-dimensional dynamical systems; 6.2 First integrals -- Jacobi's last multiplier theorem; 6.2.1 First integrals; 6.2.2 Jacobi's last multiplier theorem; 6.3 Darboux theory of integrability. 6.3.1 Algebraic particular integral -- General integral6.3.2 General integral; 6.3.3 Multiplier; 6.3.4 Algebraic particular integral and fixed points; 6.3.5 Homogeneous polynomial dynamical systems of degree m; 6.3.6 Homogeneous polynomial dynamical systems of degree two; 6.3.7 Planar polynomial dynamical systems; Differential Geometry; 7. Differential Geometry; 7.1 Concept of curves -- Kinematics vector functions; 7.1.1 Trajectory curve; 7.1.2 Instantaneous velocity vector; 7.1.3 Instantaneous acceleration vector; 7.2 Gram-Schmidt process -- Generalized Fr ́enet moving frame. Dynamics. http://id.loc.gov/authorities/subjects/sh85040316 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Dynamique. Géométrie différentielle. kinetics (dynamics) aat SCIENCE Mechanics Dynamics. bisacsh Dynamics fast Geometry, Differential fast has work: Differential geometry applied to dynamical systems (Text) https://id.oclc.org/worldcat/entity/E39PCFqrfKCtRg4KxWDFqG9KwK https://id.oclc.org/worldcat/ontology/hasWork Print version: Ginoux, Jean-Marc. Differential geometry applied to dynamical systems. Hackensack, N.J. : World Scientific, 2009 9789814277143 (OCoLC)311763235 World Scientific series on nonlinear science. Series A, Monographs and treatises ; vol. 66. http://id.loc.gov/authorities/names/no94008495 World Scientific series on nonlinear science. Series A, Monographs and treatises ; v. 66. http://id.loc.gov/authorities/names/no94008495 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305321 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305321 Volltext |
| spellingShingle | Ginoux, Jean-Marc Differential geometry applied to dynamical systems / World Scientific series on nonlinear science. Monographs and treatises ; Preface; Acknowledgments; Contents; List of Figures; List of Examples; Dynamical Systems; 1. Differential Equations; 1.1 Galileo's pendulum; 1.2 D'Alembert transformation; 1.3 From differential equations to dynamical systems; 2. Dynamical Systems; 2.1 State space -- phase space; 2.2 Definition; 2.3 Existence and uniqueness; 2.4 Flow, fixed points and null-clines; 2.5 Stability theorems; 2.5.1 Linearized system; 2.5.2 Hartman-Grobman linearization theorem; 2.5.3 Liapouno. stability theorem; 2.6 Phase portraits of dynamical systems; 2.6.1 Two-dimensional systems; 2.6.2 Three-dimensional systems. 2.7 Various types of dynamical systems2.7.1 Linear and nonlinear dynamical systems; 2.7.2 Homogeneous dynamical systems; 2.7.3 Polynomial dynamical systems; 2.7.4 Singularly perturbed systems; 2.7.5 Slow-Fast dynamical systems; 2.8 Two-dimensional dynamical systems; 2.8.1 Poincare index; 2.8.2 Poincare contact theory; 2.8.3 Poincare limit cycle; 2.8.4 Poincare-Bendixson Theorem; 2.9 High-dimensional dynamical systems; 2.9.1 Attractors; 2.9.2 Strange attractors; 2.9.3 First integrals and Lie derivative; 2.10 Hamiltonian and integrable systems; 2.10.1 Hamiltonian dynamical systems. 2.10.2 Integrable system2.10.3 K.A.M. Theorem; 3. Invariant Sets; 3.1 Manifold; 3.1.1 Definition; 3.1.2 Existence; 3.2 Invariant sets; 3.2.1 Global invariance; 3.2.2 Local invariance; 4. Local Bifurcations; 4.1 CenterManifold Theorem; 4.1.1 Center manifold theorem for flows; 4.1.2 Center manifold approximation; 4.1.3 Center manifold depending upon a parameter; 4.2 Normal FormTheorem.; 4.3 Local Bifurcations of Codimension 1; 4.3.1 Saddle-node bifurcation; 4.3.2 Transcritical bifurcation; 4.3.3 Pitchfork bifurcation; 4.3.4 Hopf bifurcation; 5. Slow-Fast Dynamical Systems; 5.1 Introduction. 5.2 Geometric Singular Perturbation Theory5.2.1 Assumptions; 5.2.2 Invariance; 5.2.3 Slow invariant manifold; 5.3 Slow-fast dynamical systems -- Singularly perturbed systems; 5.3.1 Singularly perturbed systems; 5.3.2 Slow-fast autonomous dynamical systems; 6. Integrability; 6.1 Integrability conditions, integrating factor, multiplier; 6.1.1 Two-dimensional dynamical systems; 6.1.2 Three-dimensional dynamical systems; 6.2 First integrals -- Jacobi's last multiplier theorem; 6.2.1 First integrals; 6.2.2 Jacobi's last multiplier theorem; 6.3 Darboux theory of integrability. 6.3.1 Algebraic particular integral -- General integral6.3.2 General integral; 6.3.3 Multiplier; 6.3.4 Algebraic particular integral and fixed points; 6.3.5 Homogeneous polynomial dynamical systems of degree m; 6.3.6 Homogeneous polynomial dynamical systems of degree two; 6.3.7 Planar polynomial dynamical systems; Differential Geometry; 7. Differential Geometry; 7.1 Concept of curves -- Kinematics vector functions; 7.1.1 Trajectory curve; 7.1.2 Instantaneous velocity vector; 7.1.3 Instantaneous acceleration vector; 7.2 Gram-Schmidt process -- Generalized Fr ́enet moving frame. Dynamics. http://id.loc.gov/authorities/subjects/sh85040316 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Dynamique. Géométrie différentielle. kinetics (dynamics) aat SCIENCE Mechanics Dynamics. bisacsh Dynamics fast Geometry, Differential fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85040316 http://id.loc.gov/authorities/subjects/sh85054146 |
| title | Differential geometry applied to dynamical systems / |
| title_auth | Differential geometry applied to dynamical systems / |
| title_exact_search | Differential geometry applied to dynamical systems / |
| title_full | Differential geometry applied to dynamical systems / Jean-Marc Ginoux. |
| title_fullStr | Differential geometry applied to dynamical systems / Jean-Marc Ginoux. |
| title_full_unstemmed | Differential geometry applied to dynamical systems / Jean-Marc Ginoux. |
| title_short | Differential geometry applied to dynamical systems / |
| title_sort | differential geometry applied to dynamical systems |
| topic | Dynamics. http://id.loc.gov/authorities/subjects/sh85040316 Geometry, Differential. http://id.loc.gov/authorities/subjects/sh85054146 Dynamique. Géométrie différentielle. kinetics (dynamics) aat SCIENCE Mechanics Dynamics. bisacsh Dynamics fast Geometry, Differential fast |
| topic_facet | Dynamics. Geometry, Differential. Dynamique. Géométrie différentielle. kinetics (dynamics) SCIENCE Mechanics Dynamics. Dynamics Geometry, Differential |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=305321 |
| work_keys_str_mv | AT ginouxjeanmarc differentialgeometryappliedtodynamicalsystems |