Averaging Methods in Nonlinear Dynamical Systems

  • Jan A. Sanders
  • Ferdinand Verhulst

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

Table of contents

  1. Front Matter
    Pages N2-x
  2. Jan A. Sanders, Ferdinand Verhulst
    Pages 1-8
  3. Jan A. Sanders, Ferdinand Verhulst
    Pages 9-32
  4. Jan A. Sanders, Ferdinand Verhulst
    Pages 33-66
  5. Jan A. Sanders, Ferdinand Verhulst
    Pages 67-82
  6. Jan A. Sanders, Ferdinand Verhulst
    Pages 124-142
  7. Jan A. Sanders, Ferdinand Verhulst
    Pages 143-179
  8. Jan A. Sanders, Ferdinand Verhulst
    Pages 181-235
  9. Back Matter
    Pages 236-249

About this book


In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field. The basic theory is discussed in chapters two and three. Improved results are obtained in chapter four in the case of stable limit sets. In chapter five we treat averaging over several angles; here the theory is less standardized, and even in our simplified approach we encounter many open problems. Chapter six deals with the definition of normal form. After making the somewhat philosophical point as to what the right definition should look like, we derive the second order normal form in the Hamiltonian case, using the classical method of generating functions. In chapter seven we treat Hamiltonian systems. The resonances in two degrees of freedom are almost completely analyzed, while we give a survey of results obtained for three degrees of freedom systems. The appendices contain a mix of elementary results, expansions on the theory and research problems.


Hamiltonian Systems asymptotic analysis dynamical system dynamical systems field form function functions hamiltonian system online sets solution

Authors and affiliations

  • Jan A. Sanders
    • 1
  • Ferdinand Verhulst
    • 2
  1. 1.Department of Mathematics and Computer ScienceFree UniversityAmsterdamThe Netherlands
  2. 2.Mathematical InstituteState University of UtrechtUtrechtThe Netherlands

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York 1985
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96229-0
  • Online ISBN 978-1-4757-4575-7
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site