Equilibrium States and Hausdorff Measures for Interval Maps

Abstract

For a class of piecewise monotone interval maps T (including unimodal maps with negative Schwarzian derivative) and real valued functions f of bounded variation we compare equilibrium states μ of f with Hausdorff measures v and give an integral test for the dichotomy μ ≪ v or μ ⊥ v. For certain classes of rational maps such a result was proved in [15] and [3].