Normal Forms, Bifurcations and Finiteness Problems in Differential Equations by Gert SabidussiNormal Forms, Bifurcations and Finiteness Problems in Differential Equations by Gert Sabidussi

Normal Forms, Bifurcations and Finiteness Problems in Differential Equations

byGert SabidussiEditorYulij Ilyashenko, Christiane Rousseau

Paperback | February 29, 2004

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A number of recent significant developments in the theory of differential equations are presented in an elementary fashion, many of which are scattered throughout the literature and have not previously appeared in book form, the common denominator being the theory of planar vector fields (real or complex). A second common feature is the study of bifurcations of dynamical systems. Moreover, the book links fields that have developed independently and signposts problems that are likely to become significant in the future.
The following subjects are covered: new tools for local and global properties of systems and families of systems, nonlocal bifurcations, finiteness properties of Pfaffian functions and of differential equations, geometric interpretation of the Stokes phenomena, analytic theory of ordinary differential equations and complex foliations, applications to Hilbert's 16thproblem.
Title:Normal Forms, Bifurcations and Finiteness Problems in Differential EquationsFormat:PaperbackDimensions:513 pagesPublished:February 29, 2004Publisher:Kluwer Boston Inc.Language:English

The following ISBNs are associated with this title:

ISBN - 10:1402019297

ISBN - 13:9781402019296


Table of Contents

Preface. Key to group picture. Participants. Contributors. Relations between Abelian integrals and limit cycles; M. Caubergh, R. Roussarie. Topics on singularities and bifurcations of vector fields; F. Dumortier, P. de Maesschalck. Recent advances in the analysis of divergence and singularities; J. Écalle. Local bifurcations of limit cycles, Abel equations and Liénard systems; J.-P. Françoise. Complexity of computations with Pfaffian and Noetherian functions; A. Gabrielov, N. Vorobjov. Hamiltonian bifurcations and local analytic classification; V. Gelfreich. Confluence of singular points and Stokes phenomena; A. Glutsyuk. Bifurcations of relaxation oscillations; J. Guckenheimer. Selected topics in differential equations with real and complex time; Y. Ilyashenko. Growth rate of the number of periodic points; V.Yu. Kaloshin. Normal forms, bifurcations and finiteness properties of vector fields; C. Rousseau. Aspects of planar polynomial vector fields: global versus local, real versus complex, analytic versus algebraic and geometric; D. Schlomiuk. Index.