03-138 Anna Litvak-Hinenzon and Vered Rom-Kedar

On energy surfaces and the resonance web (10207K, pdf) Mar 27, 03

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Abstract. A framework for understanding the global structure of near integrable $n$ d.o.f. systems is proposed. The goal is to reach a similar situation to the near integrable $1.5$ d.o.f. systems, where one is able in a glance of the integrable phase portrait, understand where instabilities are expected to arise under small perturbations. It is suggested that the main tool for understanding the system structure is an energy-momentum bifurcation diagram (EMBD) and generalized Fomenko graphs - the \emph{branched surfaces}. It is demonstrated that for some systems this procedure is sufficient for achieving a full qualitative description of the near-integrable dynamics. In particular, the persistent appearance of instabilities associated with resonant lower dimensional tori are discussed. The relation between the EMBD and the presentation of the energy surfaces in the frequency space is established. Finally, it is proved that topological changes in the energy surfaces topology are associated with strong resonances of lower dimensional tori.

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