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Bifurcations of Planar Vector Fields

Nilpotent Singularities and Abelian Integrals

  • Book
  • © 1991

Overview

Authors:
  1. Freddy Dumortier
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  2. Robert Roussarie
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  3. Jorge Sotomayor
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  4. Henryk Żaładek
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1480)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Introduction

    • Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 1-18

  3. Definitions and notations

    • Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 19-21

  4. Transformation into normal form

    • Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 22-27

  5. Bifurcations of codimension 1 and 2

    • Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 28-56

  6. Elementary properties

    • Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 57-84

  7. The central rescaling

    • Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 85-134

  8. Conclusions and discussion of remaining problems

    • Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 135-164

  9. Abelian integrals in unfoldings of codimension 3 singular planar vector fields

    • Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek
    Pages 165-224

  10. Back Matter

    Pages 225-226
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Bifurcations of Planar Vector Fields

  • Book Subtitle: Nilpotent Singularities and Abelian Integrals

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

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0098353

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Softcover ISBN: 978-3-540-54521-7Published: 09 October 1991

  • eBook ISBN: 978-3-540-38433-5Published: 08 December 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 232

  • Topics: Analysis

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