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Averaging Methods in Nonlinear Dynamical Systems

  • Jan A. Sanders
  • Ferdinand Verhulst
  • James Murdock

Part of the Applied Mathematical Sciences book series (AMS, volume 59)

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 1-19
  3. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 21-44
  4. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 45-65
  5. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 67-87
  6. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 89-110
  7. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 111-140
  8. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 141-170
  9. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 171-192
  10. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 193-204
  11. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 205-262
  12. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 263-283
  13. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 285-314
  14. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 315-335
  15. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 337-343
  16. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 345-352
  17. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 353-362
  18. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 363-376
  19. Jan A. Sanders, Ferdinand Verhulst, James Murdock
    Pages 377-394
  20. Back Matter
    Pages 395-433

About this book

Introduction

Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that the authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, corrections and updates in chapters on Basic Material and Asymptotics, Averaging, and Attraction. Chapters on Periodic Averaging and Hyperbolicity, Classical (first level) Normal Form Theory, Nilpotent (classical) Normal Form, and Higher Level Normal Form Theory are entirely new and represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are surveys on invariant manifolds in Appendix C and averaging for PDEs in Appendix E. Since the first edition, the book has expanded in length and the third author, James Murdock has been added.

Review of First Edition

"One of the most striking features of the book is the nice collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with profuse, illuminating diagrams." - Mathematical Reviews

Keywords

Dynamical Methods Nonlinear Systems bifurcation differential equation partial differential equation

Authors and affiliations

  • Jan A. Sanders
    • 1
  • Ferdinand Verhulst
    • 2
  • James Murdock
    • 3
  1. 1.Faculteit Exacte Wetenschappen Divisie Wiskunde en InformaticaFree University of AmsterdamAmsterdam
  2. 2.Mathematisch InstituutState University of UtrechtUtrecht
  3. 3.Dept. MathematicsIowa State University IowaAmesUSA

Bibliographic information