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Homoclinic orbits to invariant sets of quasi-integrable exact maps

Bernard, Patrick (2000), Homoclinic orbits to invariant sets of quasi-integrable exact maps, Ergodic Theory and Dynamical Systems, 20, 6, p. 1583-1601

Type
Article accepté pour publication ou publié
External document link
https://hal.archives-ouvertes.fr/hal-01251209
Date
2000
Journal name
Ergodic Theory and Dynamical Systems
Volume
20
Number
6
Publisher
Cambridge University Press
Pages
1583-1601
Metadata
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Author(s)
Bernard, Patrick cc
Abstract (EN)
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.
Subjects / Keywords
systèmes dynamiques