Ergodic Theory and Dynamical Systems

Thermodynamic formalism for certain nonhyperbolic maps

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


We establish a generalized thermodynamic formalism for certain nonhyperbolic maps with countably many preimages. We study existence and uniqueness of conformal measures and statistical properties of the equilibrium states absolutely continuous with respect to the conformal measures. We will see that such measures are not Gibbs but satisfy a version of Gibbs property (weak Gibbs measure). We apply our results to a one-parameter family of one-dimensional maps and a two-dimensional nonconformal map related to number theory. Both of them admit indifferent periodic points.

(Received July 25 1997)
(Revised July 13 1998)