ENGLISH

Bifurcations of Planar Vector Fields: Nilpotent Singularities and Abelian Integrals

By Freddy Dumortier , Robert Roussarie , Jorge Sotomayor , Henryk Żaładek (auth.)

Book information

Publisher
Springer-Verlag Berlin Heidelberg
Year
1991
ISBN
978-3-540-54521-7, 978-3-540-38433-5
DOI
10.1007/BFb0098353
Language
english
Format
PDF
Filesize
3 MB (3269237 bytes)
Series
Lecture Notes in Mathematics 1480
Edition
1
Pages
232\233
Orientation
yes
Scanned
yes
Time added
2013-08-01 04:00:00
Analysis

Description

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.

Similar books