Elementary Stability and Bifurcation Theory

  • Gérard Iooss
  • Daniel D. Joseph

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Gérard Iooss, Daniel D. Joseph
    Pages 1-3
  3. Gérard Iooss, Daniel D. Joseph
    Pages 4-12
  4. Gérard Iooss, Daniel D. Joseph
    Pages 32-44
  5. Gérard Iooss, Daniel D. Joseph
    Pages 139-156
  6. Gérard Iooss, Daniel D. Joseph
    Pages 157-185
  7. Back Matter
    Pages 281-286

About this book

Introduction

In its most general form bifurcation theory is a theory of equilibrium solutions of nonlinear equations. By equilibrium solutions we mean, for example, steady solutions, time-periodic solutions, and quasi-periodic solutions. The purpose of this book is to teach the theory of bifurcation of equilibrium solutions of evolution problems governed by nonlinear differential equations. We have written this book for the broaqest audience of potentially interested learners: engineers, biologists, chemists, physicists, mathematicians, econom­ ists, and others whose work involves understanding equilibrium solutions of nonlinear differential equations. To accomplish our aims, we have thought it necessary to make the analysis 1. general enough to apply to the huge variety of applications which arise in science and technology, and 2. simple enough so that it can be understood by persons whose mathe­ matical training does not extend beyond the classical methods of analysis which were popular in the 19th Century. Of course, it is not possible to achieve generality and simplicity in a perfect union but, in fact, the general theory is simpler than the detailed theory required for particular applications. The general theory abstracts from the detailed problems only the essential features and provides the student with the skeleton on which detailed structures of the applications must rest. It is generally believed that the mathematical theory of bifurcation requires some functional analysis and some of the methods of topology and dynamics.

Keywords

Eigenvalue Implicit function Potential bifurcation derivative differential equation eigenvector equilibrium functional analysis linear differential equation nonlinear differential equation operator solution stability topology

Authors and affiliations

  • Gérard Iooss
    • 1
  • Daniel D. Joseph
    • 2
  1. 1.Faculté des Sciences, Institut des Mathématiques et Sciences PhysiquesUniversité des NiceParc Valrose, NiceFrance
  2. 2.Department of Aerospace Engineering and MechanicsUniversity of MinnesotaMinneapolisUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-9336-8
  • Copyright Information Springer-Verlag New York 1980
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-9338-2
  • Online ISBN 978-1-4684-9336-8
  • Series Print ISSN 0172-6056
  • About this book