03-389 Heinz Hanßmann

Hamiltonian Bifurcations of Invariant Tori with a Vanishing Floquet Exponent (88K, PostScript, gzipped and uuencoded) Aug 27, 03

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Abstract. Local bifurcations of invariant tori are induced by the normal behaviour and occur where the latter changes from elliptic to hyperbolic. For invariant tori in Floquet form this is described by the Floquet exponents. When one of the Floquet exponents vanishes even the persistence of the bifurcating tori themselves is in question. With the actions conjugate to the toral angles serving as unfolding parameters, one can look for persistence of the pertinent bifurcation scenario instead. Such a study lies at the intersection of KAM theory and singularity theory. This paper presents the results of current research and ends with a speculation on how far the borders may be pushed.

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