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Bibliographic Details
Main Authors:	Hubbard, John H. 1946- (Author), West, Beverly H. (Author)
Format:	Book
Language:	English
Published:	New York u.a. Springer 1995
Series:	Texts in applied mathematics 18
Subjects:	Gewöhnliche Differentialgleichung Dynamisches System Differentialgleichung Partielle Differentialgleichung
Links:	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
Physical Description:	XIV, 601 S. zahlr. graph. Darst.
ISBN:	0387943773

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Record in the Search Index

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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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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
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volume_link	(DE-604)BV004550972 (DE-604)BV002476038
work_keys_str_mv	AT hubbardjohnh differentialequationsadynamicalsystemsapproach2 AT westbeverlyh differentialequationsadynamicalsystemsapproach2

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