Non-lacunary Gibbs Measures for Certain Fractal Repellers

Abstract

In this paper, we study non-uniformly expanding repellers constructed as the limit sets for a non-uniformly expanding dynamical systems. We prove that given a Holder continuous potential phi satisfying a summability condition, there exists non-lacunary Gibbs measure for phi, with positive Lyapunov exponents and infinitely many hyperbolic times almost everywhere. Moreover, this non-lacunary Gibbs measure is an equilibrium measure for phi.