## 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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