Differential equations and dynamical systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2001
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Texts in applied mathematics
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XIV, 555 S. graph. Darst. |
| ISBN: | 0387951164 |
Internformat
MARC
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| 100 | 1 | |a Perko, Lawrence |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Differential equations and dynamical systems |c Lawrence Perko |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
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| 490 | 1 | |a Texts in applied mathematics |v 7 | |
| 650 | 4 | |a Dynamisches System | |
| 650 | 4 | |a Gewöhnliche Differentialgleichung - Nichtlineare Differentialgleichung | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Differential equations, Nonlinear | |
| 650 | 0 | 7 | |a System von gewöhnlichen Differentialgleichungen |0 (DE-588)4116671-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804128430281719808 |
|---|---|
| adam_text | Contents
Series Preface vii
Preface ix
1 Linear Systems 1
1.1 Uncoupled Linear Systems 1
1.2 Diagonalization 6
1.3 Exponentials of Operators 10
1.4 The Fundamental Theorem for Linear Systems 16
1.5 Linear Systems in R2 19
1.6 Complex Eigenvalues 27
1.7 Multiple Eigenvalues 31
1.8 Jordan Forms 38
1.9 Stability Theory 50
1.10 Nonhomogeneous Linear Systems 58
2 Nonlinear Systems: Local Theory 63
2.1 Some Preliminary Concepts and Definitions 63
2.2 The Fundamental Existence Uniqueness Theorem 68
2.3 Dependence on Initial Conditions and Parameters 77
2.4 The Maximal Interval of Existence 84
2.5 The Flow Defined by a Differential Equation 92
2.6 Linearization 98
2.7 The Stable Manifold Theorem 102
2.8 The Hartman Grobman Theorem 116
2.9 Stability and Liapunov Functions 125
2.10 Saddles, Nodes, Foci and Centers 133
2.11 Nonhyperbolic Critical Points in R2 142
2.12 Center Manifold Theory 149
2.13 Normal Form Theory 159
2.14 Gradient and Hamiltonian Systems 166
xiv Contents
3 Nonlinear Systems: Global Theory 177
3.1 Dynamical Systems and Global Existence Theorems 178
3.2 Limit Sets and Attractors 187
3.3 Periodic Orbits, Limit Cycles and Separatrix Cycles 197
3.4 The Poincare Map 206
3.5 The Stable Manifold Theorem for Periodic Orbits 215
3.6 Hamiltonian Systems with Two Degrees of Freedom 228
3.7 The Poincare Bendixson Theory in B? 238
3.8 Lienard Systems 247
3.9 Bendixson s Criteria 258
3.10 The Poincare Sphere and the Behavior at Infinity 261
3.11 Global Phase Portraits and Separatrix Configurations 285
3.12 Index Theory 291
4 Nonlinear Systems: Bifurcation Theory 309
4.1 Structural Stability and Peixoto s Theorem 310
4.2 Bifurcations at Nonhyperbolic Equilibrium Points 328
4.3 Higher Codimension Bifurcations at Nonhyperbolic
Equilibrium Points 336
4.4 Hopf Bifurcations and Bifurcations of Limit Cycles
from a Multiple Focus 343
4.5 Bifurcations at Nonhyperbolic Periodic Orbits 355
4.6 One Parameter Families of Rotated Vector Fields 376
4.7 The Global Behavior of One Parameter Families
of Periodic Orbits 388
4.8 Homoclinic Bifurcations 393
4.9 Melnikov s Method 407
4.10 Global Bifurcations of Systems in R2 423
4.11 Second and Higher Order Melnikov Theory 443
4.12 Franchise s Algorithm for Higher Order Melnikov
Functions 457
4.13 The Takens Bogdanov Bifurcation 469
4.14 Coppel s Problem for Bounded Quadratic Systems 479
4.15 Finite Codimension Bifurcations in the Class
of Bounded Quadratic Systems 518
Appendix 534
References 547
Additional References 549
Index 555
|
| any_adam_object | 1 |
| author | Perko, Lawrence |
| author_facet | Perko, Lawrence |
| author_role | aut |
| author_sort | Perko, Lawrence |
| author_variant | l p lp |
| building | Verbundindex |
| bvnumber | BV013623571 |
| callnumber-first | Q - Science |
| callnumber-label | QA372 |
| callnumber-raw | QA372 |
| callnumber-search | QA372 |
| callnumber-sort | QA 3372 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 520 |
| classification_tum | PHY 066f PHY 013f |
| ctrlnum | (OCoLC)248026639 (DE-599)BVBBV013623571 |
| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Physik Mathematik |
| edition | 3. ed. |
| format | Book |
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| genre_facet | Aufgabensammlung |
| id | DE-604.BV013623571 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:49:07Z |
| institution | BVB |
| isbn | 0387951164 |
| language | English |
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| physical | XIV, 555 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Perko, Lawrence Verfasser aut Differential equations and dynamical systems Lawrence Perko 3. ed. New York [u.a.] Springer 2001 XIV, 555 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 7 Dynamisches System Gewöhnliche Differentialgleichung - Nichtlineare Differentialgleichung Differentiable dynamical systems Differential equations, Nonlinear System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Nichtlineare Differentialgleichung (DE-588)4205536-2 s DE-604 Dynamisches System (DE-588)4013396-5 s 2\p DE-604 Differentialgleichung (DE-588)4012249-9 s 3\p DE-604 System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 s 4\p DE-604 Texts in applied mathematics 7 (DE-604)BV002476038 7 http://www3.ub.tu-berlin.de/ihv/000879248.pdf Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009306335&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Perko, Lawrence Differential equations and dynamical systems Texts in applied mathematics Dynamisches System Gewöhnliche Differentialgleichung - Nichtlineare Differentialgleichung Differentiable dynamical systems Differential equations, Nonlinear System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4116671-1 (DE-588)4205536-2 (DE-588)4020929-5 (DE-588)4012249-9 (DE-588)4013396-5 (DE-588)4143389-0 |
| title | Differential equations and dynamical systems |
| title_auth | Differential equations and dynamical systems |
| title_exact_search | Differential equations and dynamical systems |
| title_full | Differential equations and dynamical systems Lawrence Perko |
| title_fullStr | Differential equations and dynamical systems Lawrence Perko |
| title_full_unstemmed | Differential equations and dynamical systems Lawrence Perko |
| title_short | Differential equations and dynamical systems |
| title_sort | differential equations and dynamical systems |
| topic | Dynamisches System Gewöhnliche Differentialgleichung - Nichtlineare Differentialgleichung Differentiable dynamical systems Differential equations, Nonlinear System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Dynamisches System Gewöhnliche Differentialgleichung - Nichtlineare Differentialgleichung Differentiable dynamical systems Differential equations, Nonlinear System von gewöhnlichen Differentialgleichungen Nichtlineare Differentialgleichung Gewöhnliche Differentialgleichung Differentialgleichung Aufgabensammlung |
| url | http://www3.ub.tu-berlin.de/ihv/000879248.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009306335&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002476038 |
| work_keys_str_mv | AT perkolawrence differentialequationsanddynamicalsystems |
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