Bifurcations of Planar Vector Fields : Nilpotent Singularities and Abelian Integrals / by Freddy Dumortier, Robert Roussarie, Jorge Sotomayor, Henryk Żaładek.

Format:

Book

Author/Creator:

Dumortier, Freddy, author.

Roussarie, Robert, author.

Sotomayor, Jorge, author.

Żaładek, Henryk, author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1480.

Lecture Notes in Mathematics, 0075-8434 ; 1480

Language:

English

Subjects (All):

Global analysis (Mathematics).

Analysis.

Local Subjects:

Analysis.

Physical Description:

1 online resource (VIII, 232 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1991.

System Details:

text file PDF

Summary:

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.

Contents:

Definitions and notations

Transformation into normal form

Bifurcations of codimension 1 and 2

Elementary properties

The central rescaling

Conclusions and discussion of remaining problems

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

Other Format:

Printed edition:

ISBN:

9783540384335

Access Restriction:

Restricted for use by site license.