Differential equations: a dynamical systems approach [2] Higher dimensional systems
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
Springer
1995
|
| Schriftenreihe: | Texts in applied mathematics
18 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 601 S. zahlr. graph. Darst. |
| ISBN: | 0387943773 |
Internformat
MARC
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| 245 | 1 | 0 | |a Differential equations |b a dynamical systems approach |n [2] |p Higher dimensional systems |c John H. Hubbard ; Beverly H. West |
| 264 | 1 | |a New York u.a. |b Springer |c 1995 | |
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Datensatz im Suchindex
| _version_ | 1804124602419380224 |
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| adam_text | Contents of Part II
Systems of Ordinary Differential Equations
The Higher Dimensional Theory x = f (t, x)
Series Preface v
Preface vii
Acknowledgments ix
Chapter 6 Systems of Differential Equations 1
6.1 Graphical Representation of Systems 3
6.2 Theorems for Systems of Differential Equations 12
6.3 Example: Sharks and Sardines 17
6.4 Higher Order Equations 23
6.5 Mechanical Systems with One Degree of Freedom 26
6.6 Essential Size, Conservative Laws 36
6.7 The Two Body Problem 41
6.8 Flows 47
Chapter 6 Exercises 51
Chapter 7 Systems of Linear Differential Equations 69
7.1 Linear Differential Equations in General 69
7.2 Linearity and Superposition Principles 74
7.3 Linear Differential Equations with Constant Coefficients:
Eigenvectors and Decoupling 79
7.4 Linear Differential Equations with Constant Coefficients:
Exponentials of Matrices 85
7.5 Two by Two Matrices and the Bifurcation Diagram 91
7.6 Eigenvalues and Global Behavior 101
7.7 Nonhomogeneous Linear Equations 106
Chapter 7 Exercises 113
Chapter 8 Systems of Nonlinear Differential Equations 131
8.1 Zeroes of Vector Fields and Their Linearization 132
8.2 Sources are Sources and Sinks are Sinks 141
8.3 Saddles 155
8.4 Limit Cycles 159
xii Contents
8.5 The Poincare Bendixson Theorem 162
8.6 Symmetries and Volume Preserving Equations 168
8.7 Chaos in Higher Dimensions 174
8.8 Structural Stability 181
Chapter 8 Exercises 187
Chapter 8* Structural Stability 203
8*.l Preliminaries for Structural Stability 204
8*.2 Structural Stability of Sinks and Sources 215
8*.3 Time to Pass by a Saddle 218
8*.4 Structural Stability of Limit Cycles 224
8*.5 Why Poincare Bendixson Rules Out Chaos in the Plane 236
8*.6 Structural Stability in the Plane 245
Chapter 8* Exercises 258
Chapter 9 Bifurcations 265
9.1 Saddle Node Bifurcation 271
9.2 Andronov Hopf Bifurcations 288
9.3 Saddle Connections 298
9.4 Semistable Limit Cycles 309
9.5 Bifurcation in One Parameter Families 314
9.6 Bifurcation in Two Parameter Families 318
9.7 Grand Example 335
Chapter 9 Exercises 344
Appendix L: Linear Algebra 369
LI Theory of Linear Equations: In Practice 370
L2 Theory of Linear Equations: Vocabulary 383
L3 Vector Spaces and Inner Products 402
L4 Linear Transformations and Inner Products 411
L5 Determinants and Volumes 424
L6 Eigenvalues and Eigenvectors 440
L7 Finding Eigenvalues: The QR Method 457
L8 Finding Eigenvalues: Jacobi s Method 472
Appendix L Exercises 482
Appendix L Summary 499
Appendix T: Key Theorems From Parts I and III 511
References 521
Answers to Selected Problems 523
Index 589
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:48:16Z |
| institution | BVB |
| isbn | 0387943773 |
| language | English |
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| physical | XIV, 601 S. zahlr. graph. Darst. |
| publishDate | 1995 |
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| publisher | Springer |
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| series | Texts in applied mathematics |
| series2 | Texts in applied mathematics |
| spelling | Hubbard, John H. 1946- Verfasser (DE-588)113172346 aut Differential equations a dynamical systems approach [2] Higher dimensional systems John H. Hubbard ; Beverly H. West New York u.a. Springer 1995 XIV, 601 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in applied mathematics 18 Texts in applied mathematics ... Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Dynamisches System (DE-588)4013396-5 s Gewöhnliche Differentialgleichung (DE-588)4020929-5 s Partielle Differentialgleichung (DE-588)4044779-0 s DE-604 West, Beverly H. Verfasser aut (DE-604)BV004550972 2 Texts in applied mathematics 18 (DE-604)BV002476038 18 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006776185&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hubbard, John H. 1946- West, Beverly H. Differential equations a dynamical systems approach Texts in applied mathematics Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Dynamisches System (DE-588)4013396-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| subject_GND | (DE-588)4020929-5 (DE-588)4013396-5 (DE-588)4012249-9 (DE-588)4044779-0 |
| title | Differential equations a dynamical systems approach |
| title_auth | Differential equations a dynamical systems approach |
| title_exact_search | Differential equations a dynamical systems approach |
| title_full | Differential equations a dynamical systems approach [2] Higher dimensional systems John H. Hubbard ; Beverly H. West |
| title_fullStr | Differential equations a dynamical systems approach [2] Higher dimensional systems John H. Hubbard ; Beverly H. West |
| title_full_unstemmed | Differential equations a dynamical systems approach [2] Higher dimensional systems John H. Hubbard ; Beverly H. West |
| title_short | Differential equations |
| title_sort | differential equations a dynamical systems approach higher dimensional systems |
| title_sub | a dynamical systems approach |
| topic | Gewöhnliche Differentialgleichung (DE-588)4020929-5 gnd Dynamisches System (DE-588)4013396-5 gnd Differentialgleichung (DE-588)4012249-9 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd |
| topic_facet | Gewöhnliche Differentialgleichung Dynamisches System Differentialgleichung Partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006776185&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004550972 (DE-604)BV002476038 |
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