Uniqueness of the measure of maximal entropy for singular hyperbolic flows in dimension 3 and more results on equilibrium states

Autor:	Leplaideur, Renaud
Rok vydání:	2019
Předmět:	Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	We prove that any 3-dimensional singular hyperbolic attractor admits for any H\"older continuous potential $V$ at most one equilibrium state for $V$ among regular measures. We give a condition on $V$ which ensures that no singularity can be an equilibrium state. Thus, for these $V$'s, there exists a unique equilibrium state and it is a regular measure. Applying this for $V\equiv 0$, we show that any 3-dimensional singular hyperbolic attractor admits a unique measure of maximal entropy. Comment: 43 pages 14 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1905.06202 Zobrazit plný text záznamu View this record from Arxiv