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Bifurcations of Planar Vector Fields: Nilpotent Singularities and Abelian Integrals (Lecture Notes in Mathematics) - Couverture souple

Dumortier, Freddy; Roussarie, Robert; Sotomayor, Jorge; Zoladek, Henryk

 
9783540545217: Bifurcations of Planar Vector Fields: Nilpotent Singularities and Abelian Integrals (Lecture Notes in Mathematics)
Couverture souple
ISBN 10 : 3540545212 ISBN 13 : 9783540545217
Editeur : Springer, 1991

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l'auteur

FREDDY DUMORTIER is full professor at Hasselt University (Belgium), and a member of the Royal Flemish Academy of Belgium for Science and the Arts. He was a long-term visitor at different important universities and research institutes. He is the author of many papers and his main results deal with singularities and their unfolding, singular perturbations, Lienard equations and Hilbert's 16th problem. JAUME LLIBRE is full professor at the Autonomous University of Barcelona (Spain), he is a member of the Royal Academy of Sciences and Arts of Barcelona. He was a long term visitor at different important universities and research institutes. He is the author of many papers and had a large number of Ph. D. students. His main results deal with periodic orbits, topological entropy, polynomial vector fields, Hamiltonian systems and celestial mechanics. JOAN C. ARTES is professor at the Autonomous University of Barcelona (Spain). His main results deal with polynomial vector fields, more concretely quadratic ones. He programmed, some 20 years ago, the first version of P4 (only for quadratic systems) from which the program P4 was developed with the help of Chris Herssens and Peter De Maesschalck.

À propos de la quatrième de couverture

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Springer
Date d'édition
1991
Langue
anglais
ISBN 10 
3540545212
ISBN 13 
9783540545217
Reliure
Broché
Nombre de pages
234
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