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A Remark on the Phase Transition for the Geodesic Flow of a Rank One Surface of Nonpositive Curvature by Burns, Keith; Chen, Dong is a scholarly article available to read on EtoBox.

What is A Remark on the Phase Transition for the Geodesic Flow of a Rank One Surface of Nonpositive Curvature about?

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.

Author

Burns, Keith; Chen, Dong

Published

2022

Language

EN