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A proof of existence of whiskered tori with quasi flat homoclinic intersections in a class of almost integrable Hamiltonian systems. (English) Zbl 0841.58038

In this paper a “rotator-pendulum model” is considered, i.e. a family of rotators interacting with a pendulum via a conservative force. The model is described by an \(\ell\) degrees of freedom perturbed Hamiltonian \(H_0 + \mu f\). For \(\mu = 0\) the model admits \((\ell - 1)\) dimensional invariant tori which possess homoclinic stable and unstable manifolds called “whiskers”. Here a new direct proof is given for the existence of the tori and their whiskers in the perturbed \((\mu \neq 0)\) case.

MSC:

37C75 Stability theory for smooth dynamical systems
34D10 Perturbations of ordinary differential equations
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