Nonlinear Differential Equations and Dynamical Systems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1990
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | On the subject of differential equations a great many elementary books have been written. This book bridges the gap between elementary courses and the research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed. Stability theory is developed starting with linearisation methods going back to Lyapunov and Poincaré. The global direct method is then discussed. To obtain more quantitative information the Poincaré-Lindstedt method is introduced to approximate periodic solutions while at the same time proving existence by the implicit function theorem. The method of averaging is introduced as a general approximation-normalisation method. The last four chapters introduce the reader to relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, Hamiltonian systems (recurrence, invariant tori, periodic solutions). The book presents the subject material from both the qualitative and the quantitative point of view. There are many examples to illustrate the theory and the reader should be able to start doing research after studying this book |
| Beschreibung: | 1 Online-Ressource (IX, 277p. 107 illus) |
| ISBN: | 9783642971495 9783540506287 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-642-97149-5 |
Internformat
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-97149-5 |
| format | Electronic eBook |
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| id | DE-604.BV042423154 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642971495 9783540506287 |
| issn | 0172-5939 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858571 |
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| physical | 1 Online-Ressource (IX, 277p. 107 illus) |
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| publishDate | 1990 |
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| spelling | Verhulst, Ferdinand Verfasser aut Nonlinear Differential Equations and Dynamical Systems by Ferdinand Verhulst Berlin, Heidelberg Springer Berlin Heidelberg 1990 1 Online-Ressource (IX, 277p. 107 illus) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 On the subject of differential equations a great many elementary books have been written. This book bridges the gap between elementary courses and the research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed. Stability theory is developed starting with linearisation methods going back to Lyapunov and Poincaré. The global direct method is then discussed. To obtain more quantitative information the Poincaré-Lindstedt method is introduced to approximate periodic solutions while at the same time proving existence by the implicit function theorem. The method of averaging is introduced as a general approximation-normalisation method. The last four chapters introduce the reader to relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, Hamiltonian systems (recurrence, invariant tori, periodic solutions). The book presents the subject material from both the qualitative and the quantitative point of view. There are many examples to illustrate the theory and the reader should be able to start doing research after studying this book Mathematics Global analysis (Mathematics) Mathematical physics Engineering mathematics Analysis Mathematical Methods in Physics Numerical and Computational Physics Statistical Physics, Dynamical Systems and Complexity Appl.Mathematics/Computational Methods of Engineering Mathematik Mathematische Physik 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/10.1007/978-3-642-97149-5 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 Global analysis (Mathematics) Mathematical physics Engineering mathematics Analysis Mathematical Methods in Physics Numerical and Computational Physics Statistical Physics, Dynamical Systems and Complexity Appl.Mathematics/Computational Methods of Engineering Mathematik Mathematische Physik 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 Global analysis (Mathematics) Mathematical physics Engineering mathematics Analysis Mathematical Methods in Physics Numerical and Computational Physics Statistical Physics, Dynamical Systems and Complexity Appl.Mathematics/Computational Methods of Engineering Mathematik Mathematische Physik Dynamisches System (DE-588)4013396-5 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Mathematical physics Engineering mathematics Analysis Mathematical Methods in Physics Numerical and Computational Physics Statistical Physics, Dynamical Systems and Complexity Appl.Mathematics/Computational Methods of Engineering Mathematik Mathematische Physik Dynamisches System Nichtlineare Differentialgleichung |
| url | https://doi.org/10.1007/978-3-642-97149-5 |
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