Skip to main content
SpringerLink
Log in
Book cover

Elementary Stability and Bifurcation Theory

  • Textbook
  • © 1980

Overview

Authors:
  1. Gérard Iooss

    1. Faculté des Sciences, Institut des Mathématiques et Sciences Physiques, Université des Nice, Parc Valrose, Nice, France

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Daniel D. Joseph

    1. Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (12 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Introduction

    • Gérard Iooss, Daniel D. Joseph
    Pages 1-3

  3. Equilibrium Solutions of Evolution Problems

    • Gérard Iooss, Daniel D. Joseph
    Pages 4-12

  4. Bifurcation and Stability of Steady Solutions of Evolution Equations in One Dimension

    • Gérard Iooss, Daniel D. Joseph
    Pages 13-31

  5. Imperfection Theory and Isolated Solutions Which Perturb Bifurcation

    • Gérard Iooss, Daniel D. Joseph
    Pages 32-44

  6. Stability of Steady Solutions of Evolution Equations in Two Dimensions and n Dimensions

    • Gérard Iooss, Daniel D. Joseph
    Pages 45-61

  7. Bifurcation of Steady Solutions in Two Dimensions and the Stability of the Bifurcating Solutions

    • Gérard Iooss, Daniel D. Joseph
    Pages 62-85

  8. Methods of Projection for General Problems of Bifurcation into Steady Solutions

    • Gérard Iooss, Daniel D. Joseph
    Pages 86-122

  9. Bifurcation of Periodic Solutions from Steady Ones (Hopf Bifurcation) in Two Dimensions

    • Gérard Iooss, Daniel D. Joseph
    Pages 123-138

  10. Bifurcation of Periodic Solutions in the General Case

    • Gérard Iooss, Daniel D. Joseph
    Pages 139-156

  11. Subharmonic Bifurcation of Forced T-Periodic Solutions

    • Gérard Iooss, Daniel D. Joseph
    Pages 157-185

  12. Bifurcation of Forced T-Periodic Solutions into Asymptotically Quasi-Periodic Solutions

    • Gérard Iooss, Daniel D. Joseph
    Pages 186-242

  13. Secondary Subharmonic and Asymptotically Quasi-Periodic Bifurcation of Periodic Solutions (of Hopf’s Type) in the Autonomous Case

    • Gérard Iooss, Daniel D. Joseph
    Pages 243-280

  14. Back Matter

    Pages 281-286
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Faculté des Sciences, Institut des Mathématiques et Sciences Physiques, Université des Nice, Parc Valrose, Nice, France

    Gérard Iooss

  • Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, USA

    Daniel D. Joseph

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation