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

  • Mariana Haragus
  • Gérard Iooss

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Mariana Haragus, Gérard Iooss
    Pages 1-28
  3. Mariana Haragus, Gérard Iooss
    Pages 29-91
  4. Mariana Haragus, Gérard Iooss
    Pages 93-156
  5. Mariana Haragus, Gérard Iooss
    Pages 157-237
  6. Mariana Haragus, Gérard Iooss
    Pages 239-278
  7. Back Matter
    Pages 279-329

About this book

Introduction

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.

Keywords

bifurcations center manifold reduction infinite dimensional dynamical systems normal forms travelling waves

Authors and affiliations

  • Mariana Haragus
    • 1
  • Gérard Iooss
    • 2
  1. 1.Laboratoire de MathématiquesUniversité de Franche-ComtéBesançon cedexFrance
  2. 2.Laboratoire J.A.DieudonnéIUF, Université de NiceNice Cedex 02France

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-112-7
  • Copyright Information EDP Sciences 2011
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-85729-111-0
  • Online ISBN 978-0-85729-112-7
  • About this book
Industry Sectors
Aerospace