Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/7167
Title: Topics on singularities and bifurcations of vector fields
Other Titles: NORMAL FORMS, BIFURCATIONS AND FINITENESS PROBLEMS IN DIFFERENTIAL EQUATIONS
Authors: DUMORTIER, Freddy 
DE MAESSCHALCK, Peter 
Issue Date: 2004
Publisher: Kluwer Academic Publishers
Source: Ilyashenko, Yulij & Rousseau, Christiane & Sabidussi, G. (Ed.) Proceedings of the Nato Advanced Study Institute. p. 33-86.
Series/Report: NATO SCIENCE SERIES, SERIES II: MATHEMATICS, PHYSICS AND CHEMISTRY
Series/Report no.: 137
Abstract: These notes are essentially meant to be a continuation of the lecture notes [D]. Results are presented that have mostly been obtained after 1993. In a first section we describe the classification of singularities of smooth vector fields in real 3-space up to codimension 4. Besides giving the description, attention goes to the different techniques that have been used. A second section deals with the study of the unfoldings of planar singularities and how this relates to the study of polynomial Lienard equations and of Abelian integrals. The last section deals with the study of singular perturbations for 2-dimensional vector fields, essentially from a geometric point of view. Throughout the whole text considerable emphasis is put on the one hand on blow up of singularities, and on the other hand on rescaling of families and its generalization: blow up of families.
Keywords: Liénard systems; unfoldings of singularities; bifurcations; nilpotent singularities; Abelian integrals; classification; limit cycle; family blow up; cuspidal loop; two saddle cycle; saddle loop; perturbations from elliptic Hamiltonians; singular perturbations; canard cycle; turning point
Document URI: http://hdl.handle.net/1942/7167
Link to publication: http://www.springer.com/math/dyn.+systems/book/978-1-4020-1928-9
ISBN: 978-1-4020-1928-9
DOI: 10.1007/978-94-007-1025-2_2
ISI #: 000221929600002
Category: C1
Type: Proceedings Paper
Validations: ecoom 2005
Appears in Collections:Research publications

Files in This Item:
File Description SizeFormat 
proceedings_final.pdf
  Restricted Access
692.47 kBAdobe PDFView/Open    Request a copy
Show full item record

WEB OF SCIENCETM
Citations

9
checked on May 22, 2022

Page view(s)

86
checked on May 25, 2022

Download(s)

78
checked on May 25, 2022

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.