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arXiv · 2209.11323

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

Keith Burns·Dong Chen
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Abstract

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.

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Keith Burns, Dong Chen. 2022-09-22. A remark on the phase transition for the geodesic flow of a rank one surface of nonpositive curvature. https://arxiv.org/abs/2209.11323

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