Homoclinic orbits to invariant tori in Hamiltonian systems
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hdl:2117/761
Tipus de documentArticle
Data publicació1998
Condicions d'accésAccés obert
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Abstract
We consider a perturbation of an integrable Hamiltonian system which
possesses invariant tori with coincident whiskers (like some rotators and a pendulum).
Our goal is to measure the splitting distance between the perturbed whiskers, putting
emphasis on the detection of their intersections, which give rise to homoclinic orbits
to the perturbed tori. A geometric method is presented which takes into account the
Lagrangian properties of the whiskers. In this way, the splitting distance is the gradient of a splitting potential. In the regular case (also known as a priori-unstable: the
Lyapunov exponents of the whiskered tori remain fixed), the splitting potential is well-
approximated by a Melnikov potential. This method is designed as a first step in the
study of the singular case (also known as a priori-stable: the Lyapunov exponents of the
whiskered tori approach to zero when the perturbation tends to zero).
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