Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-12-05T02:43:54.492Z Has data issue: false hasContentIssue false
  • English
  • Français

Homoclinic orbits to invariant sets of quasi-integrable exact maps

Published online by Cambridge University Press:  01 December 2000

PATRICK BERNARD
PATRICK BERNARD
Affiliation:
Université Cergy Pontoise and CEREMADE, Université, Paris Dauphine, Place du Maréchal de Lattre de Tassigny 75 775, Paris Cedex 16, France (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

The resonant tori of an integrable system are destroyed by a perturbation. If the Hamiltonian is convex, they give rise to hyperbolic lower-dimensional invariant tori or to Aubry–Mather invariant sets. Bolotin has proved the existence of homoclinic orbits to the hyperbolic tori but not to the Aubry–Mather invariant sets. We solve this problem and obtain, for each resonant frequency, the existence of an invariant set with homoclinic orbits.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 6 , December 2000 , pp. 1583 - 1601
Copyright
© 2000 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)