Bifurcations of Planar Vector Fields: Nilpotent Singularities and Abelian Integrals (Lecture Notes in Mathematics): 1480 - Brossura

Dumortier, Freddy

Brossura

ISBN 10: 3540545212 ISBN 13: 9783540545217

Casa editrice: Springer, 1991

Riassunto

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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Contenuti

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.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 1991
• Lingua: Inglese
• ISBN 10: 3540545212
• ISBN 13: 9783540545217
• Rilegatura: Copertina flessibile
• Numero di pagine: 240
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania