Thermodynamic formalism for the positive geodesic flow on the modular surface

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 The results in this paper were largely superceded by "Phase transitions for suspension flows" by Iommi and Jordan arXiv:1202.0849

arXiv commentThis 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 It was largely superceded by the paper "Phase transitions for suspension flows" by Iommi and Jordan, arXiv:1202.0849