Dynamic bifurcations. Proceedings of a conference, held in Luminy, France, March 5-10, 1990
type: Item
instance of: scholarly article
title: Dynamic bifurcations. Proceedings of a conference, held in Luminy, France, March 5-10, 1990
zbMATH Open document ID: 0756.34042
published in: Lecture Notes in Mathematics
publication date: 1992-09-18T00:00:00Z
review text: [The articles of this volume will not be indexed individually.] This volume contains a series of articles discussing various aspects of dynamic bifurcation. This theory deals with the effects arising if one considers the bifurcation parameter as varying slowly in time. This is in contrast to standard bifurcation theory, where for each value of the parameter the system (experiment) is considered to last forever. This book is an attempt to present the different articles in a unified manner. One common feature is the language of nonstandard analysis. In most articles this language is used such that it can be understood heuristically. However it seems that for a complete understanding of all articles some knowledge of nonstandard analysis is necessary. In the first article by \textit{C. Lobry}, titled Dynamic bifurcations, the fundamental questions are presented, some of the main features are illustrated by means of simple examples. Especially the phenomenon of the delay of bifurcation is explained nicely. This article puts all the articles in the volume in perspective. The relation to the main questions is illustrated. Therefore there is no need of discussing the contributions individually. Let me just mention the contributors and their titles: \textit{T. Erneux}, \textit{E. L. Reiss}, \textit{L. J. Holden} and \textit{M. Georgiu}: Slow passage through bifurcation and limit points. Asymptotic theory and applications; \textit{M. Canalis-Durand}: Formal expansion of van der Pol equation canard solution are Gevrey; \textit{V. Gautheron} and \textit{E. Isambert}: Finitely differentiable ducks and finite expansions; \textit{G. Wallet}: Overstability in arbitrary dimension; \textit{F. Diener} and \textit{M. Diener}: Maximal delay; \textit{A. Fruchard}: Existence of bifurcation delay: the discrete case; \textit{C. Baesens}: Noise effect on dynamic bifurcation: the case of a period doubling cascade; \textit{E. Benoît}: Linear dynamic bifurcation with noise; \textit{A. Delcroix…
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 00B25
Mathematics Subject Classification ID: 34-06
zbMATH DE Number: 51777
zbMATH Keywords: Luminy (France)
zbMATH Keywords: Dynamic bifurcations
zbMATH Keywords: Proceedings
zbMATH Keywords: Conference
zbMATH Keywords: dynamic bifurcation
zbMATH Keywords: nonstandard analysis
zbMATH Keywords: delay of bifurcation
zbMATH Keywords: van der Pol equation canard solution
zbMATH Keywords: finitely differentiable ducks
zbMATH Keywords: overstability
zbMATH Keywords: noise effect
zbMATH Keywords: period doubling cascade
zbMATH Keywords: asymptotic expansions
zbMATH Keywords: macroscopic rivers
reviewed by: Reiner Lauterbach
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0085019
OpenAlex ID: W4232066994
DOI: 10.1007/BFB0085019
description: scientific article; zbMATH DE number 51777