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Nonlinear Differential Equations and Dynamical Systems

  • Ferdinand Verhulst

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-X
  2. Ferdinand Verhulst
    Pages 1-6
  3. Ferdinand Verhulst
    Pages 7-24
  4. Ferdinand Verhulst
    Pages 25-37
  5. Ferdinand Verhulst
    Pages 38-58
  6. Ferdinand Verhulst
    Pages 59-68
  7. Ferdinand Verhulst
    Pages 69-82
  8. Ferdinand Verhulst
    Pages 83-95
  9. Ferdinand Verhulst
    Pages 96-109
  10. Ferdinand Verhulst
    Pages 110-121
  11. Ferdinand Verhulst
    Pages 122-135
  12. Ferdinand Verhulst
    Pages 136-165
  13. Ferdinand Verhulst
    Pages 166-172
  14. Ferdinand Verhulst
    Pages 173-192
  15. Ferdinand Verhulst
    Pages 193-223
  16. Ferdinand Verhulst
    Pages 224-247
  17. Back Matter
    Pages 248-305

About this book

Introduction

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.

Keywords

Chaos averaging methods bifurcation theory differential equations dynamical systems dynamische Systeme nonlinear systems oscillations

Authors and affiliations

  • Ferdinand Verhulst
    • 1
  1. 1.Department of MathematicsUniversity of UtrechtUtrechtThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-61453-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1996
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-60934-6
  • Online ISBN 978-3-642-61453-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site