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Bifurcations Of Planar Vector Fields: Nilpotent Singularities and Abelian Integrals by Freddy Dumortier/Robert Roussarie

Bifurcations Of Planar Vector Fields: Nilpotent Singularities and Abelian Integrals

by Freddy Dumortier , Robert Roussarie
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Book cover type: Paperback
  • ISBN13: 9783540545217
  • Binding: Paperback
  • Subject: Mathematics and Statistics
  • Publisher: Springer Verlag
  • Publisher Imprint: Springer V
  • Publication Date:
  • Pages: 238
  • Original Price: EUR 44.99
  • Language: English
  • Edition: N/A
  • Item Weight: 500 grams
  • BISAC Subject(s): Mathematical Analysis

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.

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