08-46 Henk W. Broer, Heinz Hanßmann

Hamiltonian Perturbation Theory (and Transition to Chaos) (4042K, PostScript) Mar 17, 08

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Abstract. The fundamental problem of mechanics is to study Hamiltonian systems that are small perturbations of integrable systems. But also perturbations that destroy the Hamiltonian character are important, be it to study the effect of a small amount of friction, or to further the theory of dissipative systems themselves which surprisingly often revolves around certain well-chosen Hamiltonian systems. Furthermore there are approaches like KAM theory that historically were first applied to Hamiltonian systems. Typically perturbation theory explains only part of the dynamics, and in the resulting `gaps' the orderly unperturbed motion is replaced by random or chaotic motion.

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