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.


37C75 Stability theory for smooth dynamical systems
34D10 Perturbations of ordinary differential equations
Full Text: DOI EuDML