Skip to main content
SpringerLink
Log in

Methods of Bifurcation Theory

  • Book
  • © 1982

Overview

Authors:
  1. Shui-Nee Chow

    1. Department of Mathematics, Michigan State University, East Lansing, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Jack K. Hale

    1. Division of Applied Mathematics, Brown University, Providence, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Grundlehren der mathematischen Wissenschaften (GL, volume 251)

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 89.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (14 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Introduction and Examples

    • Shui-Nee Chow, Jack K. Hale
    Pages 1-18

  3. Elements of Nonlinear Analysis

    • Shui-Nee Chow, Jack K. Hale
    Pages 19-88

  4. Applications of the Implicit Function Theorem

    • Shui-Nee Chow, Jack K. Hale
    Pages 89-114

  5. Variational Method

    • Shui-Nee Chow, Jack K. Hale
    Pages 115-167

  6. The Linear Approximation and Bifurcation

    • Shui-Nee Chow, Jack K. Hale
    Pages 168-214

  7. Bifurcation with One Dimensional Null Space

    • Shui-Nee Chow, Jack K. Hale
    Pages 215-243

  8. Bifurcation with Higher Dimensional Null Spaces

    • Shui-Nee Chow, Jack K. Hale
    Pages 244-283

  9. Some Applications

    • Shui-Nee Chow, Jack K. Hale
    Pages 284-310

  10. Bifurcation near Equilibrium

    • Shui-Nee Chow, Jack K. Hale
    Pages 311-348

  11. Bifurcation of Autonomous Planar Equations

    • Shui-Nee Chow, Jack K. Hale
    Pages 349-367

  12. Bifurcation of Periodic Planar Equations

    • Shui-Nee Chow, Jack K. Hale
    Pages 368-400

  13. Normal Forms and Invariant Manifolds

    • Shui-Nee Chow, Jack K. Hale
    Pages 401-442

  14. Higher Order Bifurcation near Equilibrium

    • Shui-Nee Chow, Jack K. Hale
    Pages 443-466

  15. Perturbation of Spectra of Linear Operators

    • Shui-Nee Chow, Jack K. Hale
    Pages 467-490

  16. Back Matter

    Pages 491-518
    Download chapter PDF
Back to top

Keywords

About this book

An alternative title for this book would perhaps be Nonlinear Analysis, Bifurcation Theory and Differential Equations. Our primary objective is to discuss those aspects of bifurcation theory which are particularly meaningful to differential equations. To accomplish this objective and to make the book accessible to a wider we have presented in detail much of the relevant background audience, material from nonlinear functional analysis and the qualitative theory of differential equations. Since there is no good reference for some of the mate­ rial, its inclusion seemed necessary. Two distinct aspects of bifurcation theory are discussed-static and dynamic. Static bifurcation theory is concerned with the changes that occur in the structure of the set of zeros of a function as parameters in the function are varied. If the function is a gradient, then variational techniques play an important role and can be employed effectively even for global problems. If the function is not a gradient or if more detailed information is desired, the general theory is usually local. At the same time, the theory is constructive and valid when several independent parameters appear in the function. In differential equations, the equilibrium solutions are the zeros of the vector field. Therefore, methods in static bifurcation theory are directly applicable.

Authors and Affiliations

  • Department of Mathematics, Michigan State University, East Lansing, USA

    Shui-Nee Chow

  • Division of Applied Mathematics, Brown University, Providence, USA

    Jack K. Hale

Bibliographic Information

  • Book Title: Methods of Bifurcation Theory

  • Authors: Shui-Nee Chow, Jack K. Hale

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-1-4613-8159-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1982

  • Softcover ISBN: 978-1-4613-8161-7Published: 08 November 2011

  • eBook ISBN: 978-1-4613-8159-4Published: 06 December 2012

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XV, 525

  • Topics: Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation