Ergodic Theory and Dynamical Systems

Weak Gibbs measures for certain non-hyperbolic systems

a1 Department of Business Administration, Sapporo University, Nishioka, Toyohira-ku, Sapporo 062, Japan


We study a weak Gibbs property of equilibrium states for potentials of weak bounded variation and for maps admitting indifferent periodic points. We further establish statistical properties of the weak Gibbs measures and bounds of their pointwise dimension. We apply our results to higher-dimensional maps (which are not necessarily conformal) with indifferent periodic points and show that their absolutely continuous finite invariant measures are weak Gibbs measures.

(Received June 25 1998)
(Revised July 1 1999)