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

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

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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Informazioni sull'autore

Peter De Maesschalck, born in 1975, has been at Hasselt University, Belgium, for much of his career. His research focuses on slow-fast systems in low dimensional systems both from a qualitative point of view and from the point of view of asymptotic expansions. Part of his research is inspired by theoretical questions such as Hilbert's 16th problem on limit cycles of polynomial systems, another part is motivated by applications of slow-fast systems in, e.g., neurological models. Freddy Dumortier, born in 1947, emeritus professor at Hasselt University, is former president of the Belgian Mathematical Society and is currently permanent secretary of the Royal Flemish Academy of Belgium for Science and the Arts. He is the author of many papers and his main results deal with singularities and their unfolding, bifurcation theory, Liénard equations, Hilbert's 16th problem, slow-fast systems and the wave speed in reaction-diffusion equations. Robert Roussarie,born in 1944, is emeritus professor of the University of Bourgogne-Franche Comté. After a career at the CNRS he was professor at the Institut de Mathématique de Bourgogne. He worked on the theory of foliations, of singularities in differential geometry, bifurcations of vector fields and finally slow-fast systems. He also contributed to applied research on ferro-resonance in electrical networks, systems of ecological populations, systems in control theory and free interface problems in combustion theory.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 1991
• Lingua: Inglese
• ISBN 10: 3540545212
• ISBN 13: 9783540545217
• Rilegatura: Copertina flessibile
• Numero di pagine: 232
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania