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

2022/09/22 by Keith Burns, Dong Chen, Burns, Keith +1
Mathematics · #37D25 #37D40 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2209.11323

openalex publication_date 2022/09/22 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28

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 μ_q for qφ^u, where φ^u is the geometric potential. We show that as q→ 1-, the weak^* limit of μ_q is the restriction of the Liouville measure to the regular set.

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