On the Aubry-Mather theory for symbolic dynamics
| dc.creator | Garibaldi, Eduardo | |
| dc.creator | Lopes, Artur O. | |
| dc.date | 2006-08-16 | |
| dc.date | 2007-07-04 | |
| dc.date.accessioned | 2026-07-07T08:13:50Z | |
| dc.date.available | 2026-07-07T08:13:50Z | |
| dc.description | We propose a new model of ergodic optimization for expansive dynamical systems: the holonomic setting. In fact, we introduce an extension of the standard model used in this theory. The formulation we consider here is quite natural if one wants a meaning for possible variations of a real trajectory under the forward shift. In another contexts (for twist maps, for instance), this property appears in a crucial way. A version of the Aubry-Mather theory for symbolic dynamics is introduced. We are mainly interested here in problems related to the properties of maximizing probabilities for the two-sided shift. Under the transitive hypothesis, we show the existence of sub-actions for Holder potentials also in the holonomic setting. We analyze then connections between calibrated sub-actions and the Mane potential. A representation formula for calibrated sub-actions is presented, which drives us naturally to a classification theorem for these sub-actions. We also investigate properties of the support of maximizing probabilities. | |
| dc.identifier | https://arxiv.org/abs/math/0608431 | |
| dc.identifier | http://arxiv.org/abs/math/0608431 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132909 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37A05; 37B10 | |
| dc.title | On the Aubry-Mather theory for symbolic dynamics | |
| dc.type | text |