Ergodic theory on coded shift spaces

Abstract

We study ergodic-theoretic properties of coded shift spaces. A coded shift space is defined as a closure of all bi-infinite concatenations of words from a fixed countable generating set. We derive sufficient conditions for the uniqueness of measures of maximal entropy and equilibrium states of Hölder continuous potentials based on the partition of the coded shift into its concatenation set (sequences that are concatenations of generating words) and its residual set (sequences added under the closure). In this case we provide a simple explicit description of the measure of maximal entropy. We also obtain flexibility results for the entropy on the concatenation and residual sets. Finally, we prove a local structure theorem for intrinsically ergodic coded shift spaces which shows that our results apply to a larger class of coded shift spaces compared to previous works by Climenhaga [9], Climenhaga and Thompson [10], [11], and Pavlov [25].