Nonlinear Differential Equations and Dynamical Systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1996
|
| Ausgabe: | Second, Revised and Expanded Edition |
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | On the subject of differential equations many elementary books have been written. This book bridges the gap between elementary courses and research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed first. Stability theory is then developed starting with linearisation methods going back to Lyapunov and Poincaré. In the last four chapters more advanced topics like relaxation oscillations, bifurcation theory, chaos in mappings and differential equations, Hamiltonian systems are introduced, leading up to the frontiers of current research: thus the reader can start to work on open research problems, after studying this book. This new edition contains an extensive analysis of fractal sets with dynamical aspects like the correlation- and information dimension. In Hamiltonian systems, topics like Birkhoff normal forms and the Poincaré-Birkhoff theorem on periodic solutions have been added. There are now 6 appendices with new material on invariant manifolds, bifurcation of strongly nonlinear self-excited systems and normal forms of Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, and is illustrated by many examples |
| Beschreibung: | 1 Online-Ressource (X, 303p. 127 illus) |
| ISBN: | 9783642614538 9783540609346 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-642-61453-8 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV042422799 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150317s1996 |||| o||u| ||||||eng d | ||
| 020 | |a 9783642614538 |c Online |9 978-3-642-61453-8 | ||
| 020 | |a 9783540609346 |c Print |9 978-3-540-60934-6 | ||
| 024 | 7 | |a 10.1007/978-3-642-61453-8 |2 doi | |
| 035 | |a (OCoLC)1165485097 | ||
| 035 | |a (DE-599)BVBBV042422799 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-384 |a DE-703 |a DE-91 |a DE-634 | ||
| 082 | 0 | |a 515.48 |2 23 | |
| 082 | 0 | |a 515.39 |2 23 | |
| 084 | |a MAT 000 |2 stub | ||
| 100 | 1 | |a Verhulst, Ferdinand |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nonlinear Differential Equations and Dynamical Systems |c by Ferdinand Verhulst |
| 250 | |a Second, Revised and Expanded Edition | ||
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1996 | |
| 300 | |a 1 Online-Ressource (X, 303p. 127 illus) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Universitext |x 0172-5939 | |
| 500 | |a On the subject of differential equations many elementary books have been written. This book bridges the gap between elementary courses and research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed first. Stability theory is then developed starting with linearisation methods going back to Lyapunov and Poincaré. In the last four chapters more advanced topics like relaxation oscillations, bifurcation theory, chaos in mappings and differential equations, Hamiltonian systems are introduced, leading up to the frontiers of current research: thus the reader can start to work on open research problems, after studying this book. This new edition contains an extensive analysis of fractal sets with dynamical aspects like the correlation- and information dimension. In Hamiltonian systems, topics like Birkhoff normal forms and the Poincaré-Birkhoff theorem on periodic solutions have been added. There are now 6 appendices with new material on invariant manifolds, bifurcation of strongly nonlinear self-excited systems and normal forms of Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, and is illustrated by many examples | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Differentiable dynamical systems | |
| 650 | 4 | |a Engineering mathematics | |
| 650 | 4 | |a Dynamical Systems and Ergodic Theory | |
| 650 | 4 | |a Numerical and Computational Physics | |
| 650 | 4 | |a Statistical Physics, Dynamical Systems and Complexity | |
| 650 | 4 | |a Appl.Mathematics/Computational Methods of Engineering | |
| 650 | 4 | |a Mathematik | |
| 650 | 0 | 7 | |a Dynamisches System |0 (DE-588)4013396-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Nichtlineare Differentialgleichung |0 (DE-588)4205536-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Dynamisches System |0 (DE-588)4013396-5 |D s |
| 689 | 0 | 1 | |a Nichtlineare Differentialgleichung |0 (DE-588)4205536-2 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-642-61453-8 |x Verlag |3 Volltext |
| 912 | |a ZDB-2-SMA |a ZDB-2-BAE | ||
| 940 | 1 | |q ZDB-2-SMA_Archive | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027858216 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153097749004288 |
|---|---|
| any_adam_object | |
| author | Verhulst, Ferdinand |
| author_facet | Verhulst, Ferdinand |
| author_role | aut |
| author_sort | Verhulst, Ferdinand |
| author_variant | f v fv |
| building | Verbundindex |
| bvnumber | BV042422799 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1165485097 (DE-599)BVBBV042422799 |
| dewey-full | 515.48 515.39 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.48 515.39 |
| dewey-search | 515.48 515.39 |
| dewey-sort | 3515.48 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-61453-8 |
| edition | Second, Revised and Expanded Edition |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03380nmm a2200553zc 4500</leader><controlfield tag="001">BV042422799</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150317s1996 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783642614538</subfield><subfield code="c">Online</subfield><subfield code="9">978-3-642-61453-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783540609346</subfield><subfield code="c">Print</subfield><subfield code="9">978-3-540-60934-6</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/978-3-642-61453-8</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1165485097</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042422799</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-384</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-634</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.48</subfield><subfield code="2">23</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.39</subfield><subfield code="2">23</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 000</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Verhulst, Ferdinand</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Nonlinear Differential Equations and Dynamical Systems</subfield><subfield code="c">by Ferdinand Verhulst</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Second, Revised and Expanded Edition</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin, Heidelberg</subfield><subfield code="b">Springer Berlin Heidelberg</subfield><subfield code="c">1996</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (X, 303p. 127 illus)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Universitext</subfield><subfield code="x">0172-5939</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">On the subject of differential equations many elementary books have been written. This book bridges the gap between elementary courses and research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed first. Stability theory is then developed starting with linearisation methods going back to Lyapunov and Poincaré. In the last four chapters more advanced topics like relaxation oscillations, bifurcation theory, chaos in mappings and differential equations, Hamiltonian systems are introduced, leading up to the frontiers of current research: thus the reader can start to work on open research problems, after studying this book. This new edition contains an extensive analysis of fractal sets with dynamical aspects like the correlation- and information dimension. In Hamiltonian systems, topics like Birkhoff normal forms and the Poincaré-Birkhoff theorem on periodic solutions have been added. There are now 6 appendices with new material on invariant manifolds, bifurcation of strongly nonlinear self-excited systems and normal forms of Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, and is illustrated by many examples</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Differentiable dynamical systems</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Engineering mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dynamical Systems and Ergodic Theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Numerical and Computational Physics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Statistical Physics, Dynamical Systems and Complexity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Appl.Mathematics/Computational Methods of Engineering</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Dynamisches System</subfield><subfield code="0">(DE-588)4013396-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineare Differentialgleichung</subfield><subfield code="0">(DE-588)4205536-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Dynamisches System</subfield><subfield code="0">(DE-588)4013396-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Nichtlineare Differentialgleichung</subfield><subfield code="0">(DE-588)4205536-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1007/978-3-642-61453-8</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-2-SMA</subfield><subfield code="a">ZDB-2-BAE</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">ZDB-2-SMA_Archive</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027858216</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042422799 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642614538 9783540609346 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858216 |
| oclc_num | 1165485097 |
| open_access_boolean | |
| owner | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (X, 303p. 127 illus) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer Berlin Heidelberg |
| record_format | marc |
| series2 | Universitext |
| spelling | Verhulst, Ferdinand Verfasser aut Nonlinear Differential Equations and Dynamical Systems by Ferdinand Verhulst Second, Revised and Expanded Edition Berlin, Heidelberg Springer Berlin Heidelberg 1996 1 Online-Ressource (X, 303p. 127 illus) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 On the subject of differential equations many elementary books have been written. This book bridges the gap between elementary courses and research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed first. Stability theory is then developed starting with linearisation methods going back to Lyapunov and Poincaré. In the last four chapters more advanced topics like relaxation oscillations, bifurcation theory, chaos in mappings and differential equations, Hamiltonian systems are introduced, leading up to the frontiers of current research: thus the reader can start to work on open research problems, after studying this book. This new edition contains an extensive analysis of fractal sets with dynamical aspects like the correlation- and information dimension. In Hamiltonian systems, topics like Birkhoff normal forms and the Poincaré-Birkhoff theorem on periodic solutions have been added. There are now 6 appendices with new material on invariant manifolds, bifurcation of strongly nonlinear self-excited systems and normal forms of Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, and is illustrated by many examples Mathematics Differentiable dynamical systems Engineering mathematics Dynamical Systems and Ergodic Theory Numerical and Computational Physics Statistical Physics, Dynamical Systems and Complexity Appl.Mathematics/Computational Methods of Engineering Mathematik Dynamisches System (DE-588)4013396-5 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Nichtlineare Differentialgleichung (DE-588)4205536-2 s 1\p DE-604 https://doi.org/10.1007/978-3-642-61453-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Verhulst, Ferdinand Nonlinear Differential Equations and Dynamical Systems Mathematics Differentiable dynamical systems Engineering mathematics Dynamical Systems and Ergodic Theory Numerical and Computational Physics Statistical Physics, Dynamical Systems and Complexity Appl.Mathematics/Computational Methods of Engineering Mathematik Dynamisches System (DE-588)4013396-5 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| subject_GND | (DE-588)4013396-5 (DE-588)4205536-2 |
| title | Nonlinear Differential Equations and Dynamical Systems |
| title_auth | Nonlinear Differential Equations and Dynamical Systems |
| title_exact_search | Nonlinear Differential Equations and Dynamical Systems |
| title_full | Nonlinear Differential Equations and Dynamical Systems by Ferdinand Verhulst |
| title_fullStr | Nonlinear Differential Equations and Dynamical Systems by Ferdinand Verhulst |
| title_full_unstemmed | Nonlinear Differential Equations and Dynamical Systems by Ferdinand Verhulst |
| title_short | Nonlinear Differential Equations and Dynamical Systems |
| title_sort | nonlinear differential equations and dynamical systems |
| topic | Mathematics Differentiable dynamical systems Engineering mathematics Dynamical Systems and Ergodic Theory Numerical and Computational Physics Statistical Physics, Dynamical Systems and Complexity Appl.Mathematics/Computational Methods of Engineering Mathematik Dynamisches System (DE-588)4013396-5 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| topic_facet | Mathematics Differentiable dynamical systems Engineering mathematics Dynamical Systems and Ergodic Theory Numerical and Computational Physics Statistical Physics, Dynamical Systems and Complexity Appl.Mathematics/Computational Methods of Engineering Mathematik Dynamisches System Nichtlineare Differentialgleichung |
| url | https://doi.org/10.1007/978-3-642-61453-8 |
| work_keys_str_mv | AT verhulstferdinand nonlineardifferentialequationsanddynamicalsystems |