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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag London Limited
About this chapter
Cite this chapter
Chen, Y., Leung, A.Y.T. (1998). Liapunov—Schmidt Reduction. In: Bifurcation and Chaos in Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-1575-5_4
Download citation
DOI: https://doi.org/10.1007/978-1-4471-1575-5_4
Publisher Name: Springer, London
Print ISBN: 978-1-4471-1577-9
Online ISBN: 978-1-4471-1575-5
eBook Packages: Springer Book Archive