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- catalog abstract "Dynamical Bifurcation Theory is concerned with the phenomena that occur in one parameter families of dynamical systems (usually ordinary differential equations), when the parameter is a slowly varying function of time. During the last decade these phenomena were observed and studied by many mathematicians, both pure and applied, from eastern and western countries, using classical and nonstandard analysis. It is the purpose of this book to give an account of these developments. The first paper, by C. Lobry, is an introduction: the reader will find here an explanation of the problems and some easy examples; this paper also explains the role of each of the other paper within the volume and their relationship to one another. CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage through Bifurcation and Limit Points. Asymptotic Theory and Applications.- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey.- V. Gautheron, E. Isambert: Finitely Differentiable Ducks and Finite Expansions.- G. Wallet: Overstability in Arbitrary Dimension.- F.Diener, M. Diener: Maximal Delay.- A. Fruchard: Existence of Bifurcation Delay: the Discrete Case.- C. Baesens: Noise Effect on Dynamic Bifurcations:the Case of a Period-doubling Cascade.- E. Benoit: Linear Dynamic Bifurcation with Noise.- A. Delcroix: A Tool for the Local Study of Slow-fast Vector Fields: the Zoom.- S.N. Samborski: Rivers from the Point ofView of the Qualitative Theory.- F. Blais: Asymptotic Expansions of Rivers.-I.P. van den Berg: Macroscopic Rivers".
- catalog contributor b3469033.
- catalog created "1991.".
- catalog date "1991".
- catalog date "1991.".
- catalog dateCopyrighted "1991.".
- catalog description "Contents: C. Lobry: Dynamic Bifurcations -- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage Through Bifurcation and Limit Points. Asymptotic Theory and Applications -- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey -- V. Gautheron, E. Isambert: Finitely Differentiable Ducks and Finite Expansions -- G. Wallet: Overstability in Arbitrary Dimension -- F. Diener, M. Diener: Maximal Delay -- A. Fruchard: Existence of Bifurcation Delay: the Discrete Case -- C. Baesens: Noise Effect on Dynamic Bifurcations: the Case of a Period-doubling Cascade -- E. Benoit: Linear Dynamic Bifurcation with Noise -- A. Delcroix: A Tool for the Local Study of Slow-fast Vector Fields: The Zoom -- S.N. Samborski: Rivers from the Point of View of the Qualitative Theory -- F. Blais: Asymptotic Expansions of Rivers -- I.P. van den Berg: Macroscopic Rivers.".
- catalog description "Dynamical Bifurcation Theory is concerned with the phenomena that occur in one parameter families of dynamical systems (usually ordinary differential equations), when the parameter is a slowly varying function of time. During the last decade these phenomena were observed and studied by many mathematicians, both pure and applied, from eastern and western countries, using classical and nonstandard analysis. It is the purpose of this book to give an account of these developments. The first paper, by C. Lobry, is an introduction: the reader will find here an explanation of the problems and some easy examples; this paper also explains the role of each of the other paper within the volume and their relationship to one another. CONTENTS: C. Lobry: Dynamic Bifurcations.- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage through Bifurcation and Limit Points. Asymptotic Theory and Applications.- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey.- V. Gautheron, E. Isambert: Finitely Differentiable Ducks and Finite Expansions.- G. Wallet: Overstability in Arbitrary Dimension.- F.Diener, M. Diener: Maximal Delay.- A. Fruchard: Existence of Bifurcation Delay: the Discrete Case.- C. Baesens: Noise Effect on Dynamic Bifurcations:the Case of a Period-doubling Cascade.- E. Benoit: Linear Dynamic Bifurcation with Noise.- A. Delcroix: A Tool for the Local Study of Slow-fast Vector Fields: the Zoom.- S.N. Samborski: Rivers from the Point ofView of the Qualitative Theory.- F. Blais: Asymptotic Expansions of Rivers.-I.P. van den Berg: Macroscopic Rivers".
- catalog description "Includes bibliogrphical references (p.[211]-219).".
- catalog extent "219 p. :".
- catalog hasFormat "Dynamic bifurcations.".
- catalog identifier "0387549005".
- catalog identifier "3540549005 :".
- catalog isFormatOf "Dynamic bifurcations.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1493.".
- catalog isPartOf "Lecture notes in mathematics ; 1493".
- catalog issued "1991".
- catalog issued "1991.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer-Verlag,".
- catalog relation "Dynamic bifurcations.".
- catalog subject "510 s 515/.35 20".
- catalog subject "Bifurcation theory Congresses.".
- catalog subject "Differentiable dynamical systems Congresses.".
- catalog subject "Differential equations Asymptotic theory Congresses.".
- catalog subject "Global analysis (Mathematics).".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1493 QA614.8".
- catalog tableOfContents "Contents: C. Lobry: Dynamic Bifurcations -- T. Erneux, E.L. Reiss, L.J. Holden, M. Georgiou: Slow Passage Through Bifurcation and Limit Points. Asymptotic Theory and Applications -- M. Canalis-Durand: Formal Expansion of van der Pol Equation Canard Solutions are Gevrey -- V. Gautheron, E. Isambert: Finitely Differentiable Ducks and Finite Expansions -- G. Wallet: Overstability in Arbitrary Dimension -- F. Diener, M. Diener: Maximal Delay -- A. Fruchard: Existence of Bifurcation Delay: the Discrete Case -- C. Baesens: Noise Effect on Dynamic Bifurcations: the Case of a Period-doubling Cascade -- E. Benoit: Linear Dynamic Bifurcation with Noise -- A. Delcroix: A Tool for the Local Study of Slow-fast Vector Fields: The Zoom -- S.N. Samborski: Rivers from the Point of View of the Qualitative Theory -- F. Blais: Asymptotic Expansions of Rivers -- I.P. van den Berg: Macroscopic Rivers.".
- catalog title "Dynamic bifurcations : proceedings of a conference held in Luminy, France, March 5-10, 1990 / E. Benoît (ed.).".
- catalog type "Conference proceedings. fast".
- catalog type "text".