Overview
- Step-by-step examples and exercises are provided throughout, illustrating the variety of possible applications
- Written by recognised experts in the field of center manifold and normal form theory
- Provides a much-needed advance level graduate text on bifurcation theory
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
From the reviews:
'This book relies on versions of the center manifold theorem that apply to infinite-dimensional dynamical systems...Chapter 4 of the book is distinctive in its presentation of normal forms for bifurcations in ‘reversible’ systems. These are systems in which there is a symmetry that reverses the orientation of time. When this symmetry is a reflection, it leads to systems that have large families of periodic orbits because forward and backward trajectories that start on the subspace must meet if they return to this subspace. This is an intricate subject, and this book makes it much more accessible than ever before. As for much of Iooss’ work throughout his career, this book gives many concrete examples of problems described by PDEs with an excellent balance between theory and applications of that theory' (SIAM Review, December 2011)
“This book relies on versions of the center manifold theorem that apply to infinite-dimensional dynamical systems. … This is an intricate subject, and this book makes it much more accessible than ever before. As for much of Iooss’ work throughout his career, this book gives many concrete examples of problems described by PDEs with an excellent balance between theory and applications of that theory.” (John Guckenheimer, SIAM Review, Vol. 53 (4), 2011)
Authors and Affiliations
Bibliographic Information
Book Title: Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems
Authors: Mariana Haragus, Gérard Iooss
Series Title: Universitext
DOI: https://doi.org/10.1007/978-0-85729-112-7
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: EDP Sciences 2011
Softcover ISBN: 978-0-85729-111-0Published: 08 December 2010
eBook ISBN: 978-0-85729-112-7Published: 23 November 2010
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XI, 329
Topics: Dynamical Systems and Ergodic Theory, Ordinary Differential Equations, Partial Differential Equations, Applications of Mathematics, Applications of Nonlinear Dynamics and Chaos Theory