Differential equations and dynamical systems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
1996
|
| Edition: | 2. ed. |
| Series: | Texts in applied mathematics
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 519 S. graph. Darst. |
| ISBN: | 0387947787 |
Staff View
MARC
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| 490 | 1 | |a Texts in applied mathematics |v 7 | |
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Record in the Search Index
| _version_ | 1804125531427307520 |
|---|---|
| adam_text | Contents
Series Preface vii
Preface to the Second Edition 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 20
1.6 Complex Eigenvalues 28
1.7 Multiple Eigenvalues 32
1.8 Jordan Forms 39
1.9 Stability Theory 51
1.10 Nonhomogeneous Linear Systems 60
2 Nonlinear Systems: Local Theory 65
2.1 Some Preliminary Concepts and Definitions 65
2.2 The Fundamental Existence Uniqueness Theorem 70
2.3 Dependence on Initial Conditions and Parameters 79
2.4 The Maximal Interval of Existence 87
2.5 The Flow Defined by a Differential Equation 95 ^
2.6 Linearization 101
2.7 The Stable Manifold Theorem 105 a , ,
2.8 The Hartman Grobman Theorem 119
2.9 Stability and Liapunov Functions 129
2.10 Saddles, Nodes, Foci and Centers 136
2.11 Nonhyperbolic Critical Points in R2 146
2.12 Center Manifold Theory 153
2.13 Normal Form Theory 162
2.14 Gradient and Hamiltonian Systems 169
xiv Contents
J^3 Nonlinear Systems: Global Theory nfb
3.1 Dynamical Systems and Global Existence Theorems 180
3.2 Limit Sets and Attractors 190
3.3 Periodic Orbits, Limit Cycles and Separatrix Cycles 200
3.4 The Poincare Map 209
3.5 The Stable Manifold Theorem for Periodic Orbits 218 i
3.6 Hamiltonian Systems with Two Degrees of Freedom 232
3.7 The Poincare Bendixson Theory in R2 242
3.8 Lienard Systems 250
3.9 Bendixson s Criteria 261
3.10 The Poincare Sphere and the Behavior at Infinity 264
3.11 Global Phase Portraits and Separatrix Configurations 290
3.12 Index Theory 294
4 Nonlinear Systems: Bifurcation Theory 311^
4.1 Structural Stability and Peixoto s Theorem 312
4.2 Bifurcations at Nonhyperbolic Equilibrium Points 325
4.3 Higher Codimension Bifurcations at Nonhyperbolic
Equilibrium Points 334
4.4 Hopf Bifurcations and Bifurcations of Limit Cycles from
a Multiple Focus 341
4.5 Bifurcations at Nonhyperbolic Periodic Orbits 351
4.6 One Parameter Families of Rotated Vector Fields 373
4.7 The Global Behavior of One Parameter Families of
Periodic Orbits 385
4.8 Homoclinic Bifurcations 390
4.9 Melnikov s Method 405
4.10 Global Bifurcations of Systems in R2 421
4.11 Second and Higher Order Melnikov Theory 442
4.12 The Takens Bogdanov Bifurcation 456
4.13 Coppel s Problem for Bounded Quadratic Systems 466
References 507
Index 513
|
| 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 | BV011042227 |
| callnumber-first | Q - Science |
| callnumber-label | QA372 |
| callnumber-raw | QA372.P47 1996 |
| callnumber-search | QA372.P47 1996 |
| callnumber-sort | QA 3372 P47 41996 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 520 SK 810 |
| classification_tum | MAT 344f |
| ctrlnum | (OCoLC)34513461 (DE-599)BVBBV011042227 |
| dewey-full | 515/.35320 515/.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 20 515/.353 |
| dewey-search | 515/.353 20 515/.353 |
| dewey-sort | 3515 3353 220 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV011042227 |
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| indexdate | 2024-07-09T18:03:02Z |
| institution | BVB |
| isbn | 0387947787 |
| language | English |
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| physical | XIV, 519 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| 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 2. ed. New York u.a. Springer 1996 XIV, 519 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 7 Equacoes diferenciais larpcal Sistemas dinamicos larpcal Differential equations, Nonlinear Differentiable dynamical systems System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Nichtlineare Differentialgleichung (DE-588)4205536-2 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 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007393783&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 Equacoes diferenciais larpcal Sistemas dinamicos larpcal Differential equations, Nonlinear Differentiable dynamical systems System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Dynamisches System (DE-588)4013396-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| subject_GND | (DE-588)4116671-1 (DE-588)4013396-5 (DE-588)4012249-9 (DE-588)4020929-5 (DE-588)4205536-2 (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 | Equacoes diferenciais larpcal Sistemas dinamicos larpcal Differential equations, Nonlinear Differentiable dynamical systems System von gewöhnlichen Differentialgleichungen (DE-588)4116671-1 gnd Dynamisches System (DE-588)4013396-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Nichtlineare Differentialgleichung (DE-588)4205536-2 gnd |
| topic_facet | Equacoes diferenciais Sistemas dinamicos Differential equations, Nonlinear Differentiable dynamical systems System von gewöhnlichen Differentialgleichungen Dynamisches System Differentialgleichung Gewöhnliche Differentialgleichung Nichtlineare Differentialgleichung Aufgabensammlung |
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| volume_link | (DE-604)BV002476038 |
| work_keys_str_mv | AT perkolawrence differentialequationsanddynamicalsystems |