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Transition along chains of invariant tori for analytic Hamiltonian systems. (Transition le long des chaînes de tores invariants pour les systèmes hamiltoniens analytiques.) (French) Zbl 0854.70011

Summary: The purpose is to prove (by constructive methods) the existence of orbits connecting the extremal tori of a transition chain, assuming that these tori possess the general normal form. The proof is based on a specific \(\lambda\)-lemma for arcs, exploiting the peculiarities of this normal form. Then we give an estimation on the transition time along the chain, using Easton’s windowing method. This approach seems to be unavoidable to compare this time to Nekhoroshev’s estimates.

MSC:

70H05 Hamilton’s equations
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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References:

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