Title: Local and Semi-Local Bifurcations in Hamiltonian Dynamical Systems: Results and Examples (Lecture Notes in Mathematics, 1893)
Publisher: Springer
Publication Date: 2006
Language: English
ISBN 10: 354038894X
ISBN 13: 9783540388944
Binding: Soft cover
Condition: New

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Synopsis

Once again KAM theory is committed in the context of nearly integrable Hamiltonian systems. While elliptic and hyperbolic tori determine the distribution of maximal invariant tori, they themselves form n-parameter families. Hence, without the need for untypical conditions or external parameters, torus bifurcations of high co-dimension may be found in a single given Hamiltonian system. The text moves gradually from the integrable case, in which symmetries allow for reduction to bifurcating equilibria, to non-integrability, where smooth parametrisations have to be replaced by Cantor sets. Planar singularities and their versal unfoldings are an important ingredient that helps to explain the underlying dynamics in a transparent way.

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