Bifurcations of Planar Vector Fields

Nilpotent Singularities and Abelian Integrals
1991
ISBN: 978-3-540-54521-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1480, 232 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 371 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Dumortier, Freddy

Zoladek, Henryk

Roussarie, Robert

Sotomayor, Jorge

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

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.