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Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems (Universitext)

by Mariana Haragus and Gýrard Iooss

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ISBN

:

9780857291110
Publisher

:

Springer
Subject

:

Mathematics, Physics
Binding

:

PAPERBACK
Pages

:

339
Year

:

2010

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~~7250.0~~

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6960.0

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An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differentialequations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.

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