Phase transitions for geodesic flows and the geometric potential

2017/04/09 by Aníbal Velozo, Velozo, Anibal · 1 citation
Mathematics · Physics and Astronomy · #37D35 #37D40 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1704.02562

openalex publication_date 2017/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the phenomenon of phase transitions for the geodesic flow on some geometrically finite negatively curved manifolds. We define a class of potentials going slowly to zero through the cusps of M for which the pressure map exhibits a phase transition. By a careful choice of the metric at the cusp we construct a geometrically finite manifold for which the geometric potential (or unstable Jacobian) exhibits a phase transition. Our results apply, in particular, to the geodesic flow on an M-puncture sphere, for every M≥ 3, and a suitable choice of Riemannian metric.

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