A remark on the phase transition for the geodesic flow of a rank one surface of nonpositive curvature

Autor:	Burns, Keith, Chen, Dong
Rok vydání:	2022
Předmět:	Mathematics - Dynamical Systems 37D25 37D40
Druh dokumentu:	Working Paper
Popis:	For any rank 1 nonpositively curved surface $M$, it was proved by Burns-Climenhaga-Fisher-Thompson that for any $q<1$, there exists a unique equilibrium state $\mu_q$ for $q\varphi^u$, where $\varphi^u$ is the geometric potential. We show that as $q\to 1-$, the weak$^*$ limit of $\mu_q$ is the restriction of the Liouville measure to the regular set.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2209.11323 Zobrazit plný text záznamu View this record from Arxiv