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 publiéExternal document link
https://hal.archives-ouvertes.fr/hal-01251209Date
2000Journal name
Ergodic Theory and Dynamical SystemsVolume
20Number
6Publisher
Cambridge University Press
Pages
1583-1601
Metadata
Show full item recordAbstract (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 dynamiquesRelated items
Showing items related by title and author.
-
Bernard, Patrick (2002) Article accepté pour publication ou publié
-
Bernard, Patrick (2003) Article accepté pour publication ou publié
-
Jézéquel, Tiphaine; Bernard, Patrick; Lombardi, Eric (2016) Article accepté pour publication ou publié
-
Bernardi, Olga; Florio, Anna; Wiseman, Jim (2022) Article accepté pour publication ou publié
-
Aslani, Shahriar; Bernard, Patrick (2020) Document de travail / Working paper