Thermodynamic formalism for the positive geodesic flow on the modular surface

2010/09/23 by Godofredo Iommi, Iommi, Godofredo · 1 citation
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Theoretical and Computational Physics #math.DS

paper · pdf · doi:10.48550/arxiv.1009.4623

This note is not intended for publication. It was largely superceded by the paper "Phase transitions for suspension flows" by Iommi and Jordan, arXiv:1202.0849

openalex publication_date 2010/09/23 · arxiv created 2012/02/16 · arxiv updated 2012/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we study the thermodynamic formalism for the positive geodesic flow on the modular surface. We define the pressure and prove the variational principle. We also establish conditions for the the pressure to be real analytic and for the potentials to have unique equilibrium states. The results in this paper were largely superceded by "Phase transitions for suspension flows" by Iommi and Jordan arXiv:1202.0849

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• Phase transitions for suspension flows

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