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Near strongly resonant periodic orbits in a Hamiltonian system

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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

Topics: Q
Publisher: NATL ACAD SCIENCES
OAI identifier: oai:wrap.warwick.ac.uk:10435
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