98-660 Luigi Chierchia, Enrico Valdinoci

A note on the construction of Hamiltonian trajectories along heteroclinic chain (46K, LaTeX 2.09) Oct 16, 98

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Abstract. We revisit chapter 8 of L. Chierchia, G. Gallavotti, Drift and diffusion in phase space, Ann. Inst. Henri Poincare', with the purpose of providing a short, simple proof of the existence of Hamiltonian trajectories arbitrarily close to a chain of heteroclinic orbits connecting whiskered tori. We also discuss a characterization of transversality for whiskers that are graphs ``over the angles". In Appendix we consider a model problem (a ``standard chain of transition tori") and prove that the ``drifting times" are proportional, for such a model, to a power of the number of tori forming the chain (in the perturbative case, this would correspond to drifting times which are polynomial in the inverse of the perturbation parameter).

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