Equilibrium states of almost Anosov diffeomorphisms

Abstract

We develop a thermodynamic formalism for a class of diffeomorphisms of a torus that are "almost-Anosov". In particular, we use a Young tower construction to prove the existence and uniqueness of equilibrium states for a collection of non-H\"older continuous geometric potentials over almost Anosov systems with an indifferent fixed point, as well as prove exponential decay of correlations and the central limit theorem for these equilibrium measures.