Bifurcations of Planar Vector Fields

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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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.

• Vector field
• bifurcation
• differential equation
• dynamical systems
• integral
• ordinary differential equation

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