Continuous spectrum on laminations over Aubry-Mather sets
| dc.creator | Fayad, Bassam | |
| dc.date | 2004-04-07 | |
| dc.date.accessioned | 2026-07-07T05:07:16Z | |
| dc.date.available | 2026-07-07T05:07:16Z | |
| dc.description | If we perturb a completely integrable Hamiltonian system with two degrees of freedom, the perturbed flow might display, on every energy level, invariant sets that are laminations over Aubry-Mather sets of a Poincaré section of the flow. Each one of these laminations carry a unique invariant probability measure for the flow on which mixing is impossible in this low dimensional frame. We prove that if the Aubry-Mather set has exactly one orbit of gaps and is hyperbolic then the special flow over it with any smooth ceiling function will be conjugate to a suspension with a constant ceiling function, failing hence to be weak mixing or even topologically weak mixing. To the contrary, if the Aubry-Mather set has more than one orbit of gaps with at least two in a general position then the special flow over it will in general be weak mixing. | |
| dc.identifier | https://arxiv.org/abs/math/0404168 | |
| dc.identifier | http://arxiv.org/abs/math/0404168 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70795 | |
| dc.subject | Dynamical Systems | |
| dc.title | Continuous spectrum on laminations over Aubry-Mather sets | |
| dc.type | text |