ENGLISH

Qualitative Theory of Planar Differential Systems

By Freddy Dumortier , Jaume Llibre , Joan C. Artés

Book information

Publisher
Springer
Year
2006
ISBN
9783540328933, 3-540-32893-9
Open Library ID
OL9056374M
Language
english
Format
PDF
Filesize
4 MB (4412013 bytes)
Series
Universitext
Edition
1
Pages
316\316
Library
mexmat
Time added
2009-07-20 03:45:11

Description

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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