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

by Haragus, Mariana.
Authors: Iooss, Gérard.%author. | SpringerLink (Online service) Series: Universitext Physical details: XI, 329 p. online resource. ISBN: 0857291122 Subject(s): Mathematics. | Differentiable dynamical systems. | Differential Equations. | Differential equations, partial. | Mathematics. | Dynamical Systems and Ergodic Theory. | Ordinary Differential Equations. | Partial Differential Equations. | Applications of Mathematics. | Nonlinear Dynamics.
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E-Book E-Book AUM Main Library 515.39 (Browse Shelf) Not for loan

Elementary Bifurcations -- Center Manifolds -- Normal Forms -- Reversible Bifurcations -- Applications -- Appendix.

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 differential equations 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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