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

Dumortier, Freddy

Softcover

ISBN 10: 3540545212 ISBN 13: 9783540545217

Verlag: Springer, 1991

Inhaltsangabe

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.

Über diesen Titel

Über die Autorin bzw. den Autor

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 16^th 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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 1991
• Sprache: Englisch
• ISBN 10: 3540545212
• ISBN 13: 9783540545217
• Einband: Taschenbuch
• Anzahl der Seiten: 240
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland