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Lecture Notes in Mathematics

Bifurcations of Planar Vector Fields

Nilpotent Singularities and Abelian Integrals

Authors: Dumortier, F., Roussarie, R., Sotomayor, J., Zoladek, H.

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About this book

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.

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-540-38433-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-540-54521-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Bifurcations of Planar Vector Fields
Book Subtitle
Nilpotent Singularities and Abelian Integrals
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1480
Copyright
1991
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-38433-5
DOI
10.1007/BFb0098353
Softcover ISBN
978-3-540-54521-7
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 232
Topics