Multi-dimensional maps with infinite invariant measures and countable state sofic shifts

Abstract

We study multi-dimensional maps on bounded domains of R d satisfying the finite range structure (FRS) condition, which leads us to countable state sofic systems. Such maps admit σ-finite ergodic invariant measures equivalent to Lebesgue measures under the local Renyi condition. In this paper we show that several ergodic properties still hold even if such invariant measures are infinite. We also investigate the validity of Rohlin's entropy formula and of a variational principle for entropy.