Abstract
This chapter and Chapter IX use the theory of normal forms developed in Chapter VI. They contain an introduction to generic bifurcation theory and its applications. Bifurcation theory has grown into a vast subject with a large literature; so, this chapter can only present the basics of the theory. The primary focus of this chapter is the study of periodic solutions—their existence and evolution. Periodic solutions abound in Hamiltonian systems. In fact, a famous Poincaré conjecture is that periodic solutions are dense in a generic Hamiltonian system, a point that was established in the C 1 case by Pugh and Robinson (1977).
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
© 1992 Springer Science+Business Media New York
About this chapter
Cite this chapter
Meyer, K.R., Hall, G.R. (1992). Bifurcations of Periodic Orbits. In: Introduction to Hamiltonian Dynamical Systems and the N-Body Problem. Applied Mathematical Sciences, vol 90. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4073-8_8
Download citation
DOI: https://doi.org/10.1007/978-1-4757-4073-8_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-4075-2
Online ISBN: 978-1-4757-4073-8
eBook Packages: Springer Book Archive