Dynamic bifurcations: proceedings of a conference held in Luminy, France, March 5-10, 1990

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Springer-Verlag, 1991 - Mathematics - 219 pages
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Dynamical Bifurcation Theory is concerned with the phenomenathat occur in one parameter families of dynamical systems(usually ordinary differential equations), when theparameter is a slowly varying function of time. During thelast decade these phenomena were observed and studied bymany mathematicians, both pure and applied, from eastern andwestern countries, using classical and nonstandard analysis.It is the purpose of this book to give an account of thesedevelopments. The first paper, by C. Lobry, is anintroduction: the reader will find here an explanation ofthe problems and some easy examples; this paper alsoexplains the role of each of the other paper within thevolume and their relationship to one another.CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L.Reiss, L.J. Holden, M. Georgiou: Slow Passage throughBifurcation and Limit Points. Asymptotic Theory andApplications.- M. Canalis-Durand: Formal Expansion of vander Pol Equation Canard Solutions are Gevrey.- V. Gautheron,E. Isambert: Finitely Differentiable Ducks and FiniteExpansions.- G. Wallet: Overstability in ArbitraryDimension.- F.Diener, M. Diener: Maximal Delay.- A.Fruchard: Existence of Bifurcation Delay: the DiscreteCase.- C. Baesens: Noise Effect on Dynamic Bifurcations:theCase of a Period-doubling Cascade.- E. Benoit: LinearDynamic Bifurcation with Noise.- A. Delcroix: A Tool for theLocal Study of Slow-fast Vector Fields: the Zoom.- S.N.Samborski: Rivers from the Point ofView of the QualitativeTheory.- F. Blais: Asymptotic Expansions of Rivers.-I.P.van den Berg: Macroscopic Rivers

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Contents

Dynamic Bifurcations
1
Slow Passage Through Bifurcation and Limit Points
7
Asymptotic Theory and Applications
14
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