Item description for Qualitative Theory of Planar Differential Systems (Universitext) by Freddy Dumortier, Jaume Llibre & Joan C. Artes...
The book deals essentially with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability. In the last two chapters the performant software tool P4 is introduced.From the start, differential systems are represented by vector fields enabling, in full strength, a dynamical systems approach. All essential notions, including invariant manifolds, normal forms, desingularization of singularities, index theory and limit cycles, are introduced and the main results are proved for smooth systems with the necessary specifications for analytic and polynomial systems.The book is very appropriate for a first course in dynamical systems. Not only does it provide simple and appropriate proofs, but it also contains a lot of exercises and presents a survey of interesting results with the necessary references to the literature.
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Est. Packaging Dimensions: Length: 0.75" Width: 6" Height: 9" Weight: 1.1 lbs.
Release Date Oct 9, 2006
ISBN 3540328939 ISBN13 9783540328933
Availability 87 units. Availability accurate as of Oct 22, 2016 03:17.
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More About Freddy Dumortier, Jaume Llibre & Joan C. Artes
Freddy Dumortier is full professor at Hasselt University (Belgium), he is a member of the Royal Flemish Academy of Belgium for Sciences and the Arts, and he was president of the Belgian Mathematical Society. He was a long term visitor at different important universities and research institutes. He is the author of many papers and was the organizer of different international conferences among which Equadiff 2003 in Hasselt. 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. He was the organizer of different international conferences among which four HAMSYS meetings and five encounters in Dynamical Systems. His main results deal with periodic orbits, topological entropy, polynomial vector fields, Hamiltonian systems and celestial mechanics. Joan C. Artis is professor at the Autonomous University of Barcelona (Spain). His main results deal with polynomial vector fields, more concretely quadratic ones. He programmed the first version of P4 (only for quadratic systems) in the 80's from which the program P4 was developed with the help of Chris Herssens and Peter De Maesschalck.