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Liapunov—Schmidt Reduction

  • Yushu Chen
  • Andrew Y. T. Leung

Abstract

The theory and application of bifurcation are presented in this chapter and chapter 5. This chapter describes the basic concepts of bifurcation in ordinary differential equations, Liapunov—Schmidt reduction (LS reduction for short), singularity theory and applications of all these theories. Chapter 5 introduces the centre manifold theorem and the normal form of vector fields. Chapter 6 presents the Hopf bifurcation and double zero eigenvalues. Chapter 7 explains the applications of the averaging method in bifurcation theory.

Keywords

Hopf Bifurcation Bifurcation Diagram Implicit Function Theorem Heteroclinic Orbit Pitchfork Bifurcation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag London Limited 1998

Authors and Affiliations

  • Yushu Chen
    • 1
  • Andrew Y. T. Leung
    • 2
  1. 1.Department of MechanicsTianjin UniversityTianjinChina
  2. 2.Manchester School of Engineering, Simon BuildingUniversity of ManchesterManchesterUK

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