Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem

  • Robert Roussarie

Part of the Modern Birkhäuser Classics book series (MBC)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Robert Roussarie
    Pages 1-15
  3. Robert Roussarie
    Pages 17-31
  4. Robert Roussarie
    Pages 33-49
  5. Robert Roussarie
    Pages 51-90
  6. Robert Roussarie
    Pages 91-149
  7. Back Matter
    Pages 193-204

About this book

Introduction

In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets.

The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations. 

- - -

The book as a whole is a well-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in recently developed methods. The book, reflecting the state of the art, can also be used for teaching special courses.
(Mathematical Reviews)

 

Keywords

bifurcation diagrams desingularization theory differential equations dynamical systems limit cycles limit periodic sets singular limit sets bifurcation differential equation

Authors and affiliations

  • Robert Roussarie
    • 1
  1. 1.Department of MathematicsUniversity of BourgogneDijon CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0718-0
  • Copyright Information Springer Basel 1998
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0348-0717-3
  • Online ISBN 978-3-0348-0718-0
  • Series Print ISSN 2197-1803
  • Series Online ISSN 2197-1811
  • About this book