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arXiv · 1704.02562

Phase transitions for geodesic flows and the geometric potential

Anibal Velozo
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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 $M\ge 3$, and a suitable choice of Riemannian metric.

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Anibal Velozo. 2018-04-25. Phase transitions for geodesic flows and the geometric potential. https://arxiv.org/abs/1704.02562

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