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Normal Forms, Bifurcations and Finiteness Problems in Differential Equations : NATO Science Series II - Gert Sabidussi

Normal Forms, Bifurcations and Finiteness Problems in Differential Equations

NATO Science Series II

By: Gert Sabidussi (Adapted By), Yulij Ilyashenko (Editor), Christiane Rousseau (Editor)

Hardcover

Published: 29th February 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 16th problem. Readership: Graduate students, postdocs and researchers in dynamical systems with a minimum background of a one-year course on nonlinear differential equations. 'Skeletal metastases are both a common and devastating consequence of a spectrum of cancers. Significant advances have occurred in our understanding of the pathobiology of this process. This text provides a comprehensive review of current investigative findings and their clinical implications.' Steven T. Rosen, M.D. Series Editor

Preface
Key to group picture
Participants
Contributors
Relations between Abelian integrals and limit cyclesp. 1
Topics on singularities and bifurcations of vector fieldsp. 33
Recent advances in the analysis of divergence and singularitiesp. 87
Local bifurcations of limit cycles, Abel equations and Lienard systemsp. 187
Complexity of computations with Pfaffian and Noetherian functionsp. 211
Hamiltonian bifurcations and local analytic classificationp. 251
Confluence of singular points and Stokes phenomenap. 267
Bifurcations of relaxation oscillationsp. 295
Selected topics in differential equations with real and complex timep. 317
Growth rate of the number of periodic pointsp. 355
Lectures on meromorphic flat connectionsp. 387
Normal forms, bifurcations, and finiteness properties of vector fieldsp. 431
Aspects of planar polynomial vector fields: global versus local, real versus complex, analytic versus algebraic and geometricp. 471
Indexp. 511
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9781402019289
ISBN-10: 1402019289
Series: NATO Science Series II : Book 137
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 513
Published: 29th February 2004
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.4 x 17.0  x 3.18
Weight (kg): 2.05