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

Gentile, Guido

Forum Math. 7, No. 6, 709-753 (1995).

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.

Reviewer: M.Farkas (Budapest)

MSC:

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

Keywords:

whiskered tori; quasi flat homoclinic intersections; almost integrable Hamiltonian systems; existence