Luigi Chierchia, Enrico Valdinoci
A note on the construction of Hamiltonian trajectories along
heteroclinic chain
(46K, LaTeX 2.09)
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).