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Bifurcations of Planar Vector Fields

Nilpotent Singularities and Abelian Integrals

  • Authors
  • Freddy Dumortier
  • Robert Roussarie
  • Jorge Sotomayor
  • Henryk Żaładek

Part of the Lecture Notes in Mathematics book series (LNM, volume 1480)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 1-18
  3. Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 19-21
  4. Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 22-27
  5. Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 28-56
  6. Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 57-84
  7. Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 85-134
  8. Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 135-164
  9. Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 165-224
  10. Back Matter
    Pages 225-226

About this book

Introduction

The book reports on recent work by the authors on the bifurcation structure of singular points of planar vector fields whose linear parts are nilpotent. The bifurcation diagrams of the most important codimension-three cases are studied in detail. The results presented reach the limits of what is currently known on the bifurcation theory of planar vector fields. While the treatment is geometric, special analytical tools using abelian integrals are needed, and are explicitly developed. The rescaling and normalization methods are improved for application here. The reader is assumed to be familiar with the elements of Bifurcation and Dynamical Systems Theory. The book is addressed to researchers and graduate students working in Ordinary Differential Equations and Dynamical Systems, as well as anyone modelling complex multiparametric phenomena.

Keywords

Vector field bifurcation differential equation dynamical systems integral ordinary differential equation

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0098353
  • Copyright Information Springer-Verlag Berlin Heidelberg 1991
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-54521-7
  • Online ISBN 978-3-540-38433-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site