Methods In Equivariant Bifurcations And Dynamical Systems : Advanced Nonlinear Dynamics - Pascal Chossat

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Methods In Equivariant Bifurcations And Dynamical Systems

By: Pascal Chossat, Reiner Lauterbach

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Hardcover | 1 March 2000

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Hardcover
420 Pages

Dimensions(cm)
22.23 x 16.51 x 1.91

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This invaluable book presents a comprehensive introduction to bifurcation theory in the presence of symmetry, an applied mathematical topic which has developed considerably over the past twenty years and has been very successful in analysing and predicting pattern formation and other critical phenomena in most areas of science where nonlinear models are involved, like fluid flow instabilities, chemical waves, elasticity and population dynamics.The book has two aims. One is to expound the mathematical methods of equivariant bifurcation theory. Beyond the classical bifurcation tools, such as center manifold and normal form reductions, the presence of symmetry requires the introduction of the algebraic and geometric formalism of Lie group theory and transformation group methods. For the first time, all these methods in equivariant bifurcations are presented in a coherent and self-consistent way in a book.The other aim is to present the most recent ideas and results in this theory, in relation to applications. This includes bifurcations of relative equilibria and relative periodic orbits for compact and noncompact group actions, heteroclinic cycles and forced symmetry-breaking perturbations. Although not all recent contributions could be included and a choice had to be made, a rather complete description of these new developments is provided. At the end of every chapter, exercises are offered to the reader.

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Preface
Symmetries in ODE's and PDE's	p. 1
Equivariant bifurcations, a first look	p. 35
Invariant manifolds and normal forms	p. 71
Linear Lie Group Actions	p. 103
The equivariant structure of bifurcation equations	p. 155
Reduction techniques for equivariant systems	p. 187
Relative equilibria and relative periodic orbits	p. 213
Bifurcations in Equivariant Systems	p. 263
Heteroclinic cycles	p. 309
Perturbation of equivarient systems	p. 353
Miscellanea on the group SO(3)	p. 375
Translation table for the subgroups of SO(3)	p. 383
Bibliography	p. 385
Index	p. 401
Table of Contents provided by Blackwell. All Rights Reserved.

Methods In Equivariant Bifurcations And Dynamical Systems

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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