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

## Haragus, Mariana; Iooss, Gerard

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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 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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Recensione:

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)

Contenuti:

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

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## 1.Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems (Paperback)

Editore: Springer London Ltd, United Kingdom (2011)
ISBN 10: 0857291114 ISBN 13: 9780857291110
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Descrizione libro Springer London Ltd, United Kingdom, 2011. Paperback. Condizione libro: New. 231 x 155 mm. Language: English . Brand New Book ***** Print on Demand *****.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. Codice libro della libreria AAV9780857291110

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

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

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Descrizione libro Springer, 2010. Paperback. Condizione libro: NEW. 9780857291110 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0286197

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

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## 5.Local Bifurcations, Center Manifolds, and Normal Forms in Infinite-Dimensional Dynamical Systems (Paperback)

Editore: Springer London Ltd, United Kingdom (2011)
ISBN 10: 0857291114 ISBN 13: 9780857291110
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Descrizione libro Springer London Ltd, United Kingdom, 2011. Paperback. Condizione libro: New. 2011. 231 x 155 mm. Language: English . Brand New Book ***** Print on Demand *****. 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. Codice libro della libreria AAV9780857291110

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

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Descrizione libro Springer London Ltd 2010-12-08, England, 2010. paperback. Condizione libro: New. Codice libro della libreria 9780857291110

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

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

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## 9.Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems

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Descrizione libro Springer-Verlag Gmbh Feb 2011, 2011. Taschenbuch. Condizione libro: Neu. 234x156x27 mm. Neuware - 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. 325 pp. Englisch. Codice libro della libreria 9780857291110

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

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Descrizione libro Springer, 2010. Paperback. Condizione libro: New. book. Codice libro della libreria 0857291114

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