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math.DS2014★ 9 cited
Dynamics of the dominant Hamiltonian, with applications to Arnold diffusion
Vadim Kaloshin, Ke Zhang
It is well known that instabilities of nearly integrable Hamiltonian systems occur around resonances. Dynamics near resonances of these systems is well approximated by the associat…
math.DS2012★ 11 cited
Normally hyperbolic invariant manifolds near strong double resonance
Vadim Kaloshin, Ke Zhang
In the present paper we consider a generic perturbation of a nearly integrable system of and a half degrees of freedom , with a strictly convex…