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The transfer lemma for Graff tori and Arnold diffusion time. (English) Zbl 1018.37040

It is shown that Graff tori satisfy the transitivity property. The proof is shown on a so-called transfer lemma. The result allows us to compute the Arnold diffusion time along transition chains for initially hyperbolic Hamiltonian systems. It is furthermore proved that this time is polynomial in the inverse of the perturbing parameter.

MSC:

37J40 Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
54H20 Topological dynamics (MSC2010)
70K50 Bifurcations and instability for nonlinear problems in mechanics
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