Methods In Equivariant Bifurcations And Dynamical Systems (Advanced Series in Nonlinear Dynamics)

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9789810238285: Methods In Equivariant Bifurcations And Dynamical Systems (Advanced Series in Nonlinear Dynamics)
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Book by Pascal Chossat Reiner Lauterbach

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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.

Reseña del editor:

A comprehensive introduction to bifurcation theory in the presence of symmetry, an applied mathematical topic which has developed considerably since the late 1970s. The book has two aims. One is to expound the mathematical methods of equivariant bifurcation theory. Beyond the classical bifurcation tools, such as centre 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. The other aim is to present the most recent ideas and results in this theory, in relation to applications. This includes bifurcation 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 developments is provided. At the end of every chapter, exercises are offered to the reader.

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Pascal Chossat; Reiner Lauterbach
Publicado por World Scientific Publishing Company (2000)
ISBN 10: 9810238282 ISBN 13: 9789810238285
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(RICHMOND, TX, Estados Unidos de America)

Descripción World Scientific Publishing Company, 2000. Hardcover. Condición: Good. Nº de ref. del artículo: SONG9810238282

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