Near strongly resonant periodic orbits in a Hamiltonian system.

Gelfreich, Vassili · Proc Natl Acad Sci U S A · 2002

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Abstract

We study an analytic Hamiltonian system near a strongly resonant periodic orbit. We introduce a modulus of local analytic classification. We provide asymptotic formulae for the exponentially small splitting of separatrices for bifurcating hyperbolic periodic orbits. These formulae confirm a conjecture formulated by V. I. Arnold in the early 1970s.