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

Keith Burns; Dong Chen

doi:10.1080/14689367.2023.2229752

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

Keith Burns, Dong Chen^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

For any rank 1 nonpositively curved surface (Formula presented.), it was proved by Burns-Climenhaga-Fisher-Thompson that for any (Formula presented.), there exists a unique equilibrium state (Formula presented.) for (Formula presented.), where (Formula presented.) is the geometric potential. We show that as (Formula presented.), the weak-* limit of (Formula presented.) is the restriction of the Liouville measure to the regular set.

Original language	English (US)
Pages (from-to)	1-4
Number of pages	4
Journal	Dynamical Systems
Volume	39
Issue number	1
DOIs	https://doi.org/10.1080/14689367.2023.2229752
State	Published - 2024

Keywords

Equilibrium states
geodesic flow
phase transition

ASJC Scopus subject areas

General Mathematics
Computer Science Applications

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10.1080/14689367.2023.2229752

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AB - For any rank 1 nonpositively curved surface (Formula presented.), it was proved by Burns-Climenhaga-Fisher-Thompson that for any (Formula presented.), there exists a unique equilibrium state (Formula presented.) for (Formula presented.), where (Formula presented.) is the geometric potential. We show that as (Formula presented.), the weak-* limit of (Formula presented.) is the restriction of the Liouville measure to the regular set.

KW - Equilibrium states

KW - geodesic flow

KW - phase transition

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

Abstract

Keywords

ASJC Scopus subject areas

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