Namazi, M. Julien (2023) Formalisme thermodynamique dans les systèmes dynamiques hyperboliques PRE - Projet de recherche, ENSTA.
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Résumé
In this research internship we will firstly be interested in thermodynamical formalism : we will construct topological entropy, measure entropy and the variationnal principles. During those chapters we will emphasize on symbolic dynamics because it is a dynamics that we understand very well. Then we will properly define what hyperbolic dynamics is. Using a localization procedure we will be interested in the expansivity of this dynamics and in the stable manifold theorem. Finally we will show the existence of symbolic coding for a particular class of hyperbolic dynamics : Anosov diffeomorphism.
| Type de document: | Rapport ou mémoire (PRE - Projet de recherche) |
|---|---|
| Mots-clés libres: | Topological dynamics, ergodic theory, topological and measure entropy, topological and measure pressure, variationnal principle, equilibrium measure, hyperbolic dynamics, stable and unstable manifolds, Markov partitions, Anosov diffeomorphism. |
| Sujets: | Mathématiques et leurs applications |
| Code ID : | 9710 |
| Déposé par : | Julien NAMAZI |
| Déposé le : | 01 sept. 2023 14:31 |
| Dernière modification: | 01 sept. 2023 14:31 |
