Measures of Maximal Entropy on Coded Shift Spaces: Uniqueness and Computability

Prof. Christian Wolf
Executive Officer and Professor
CUNY Graduate Center and City College

In this talk, we present results about the uniqueness and computability of measures of maximal entropy on coded shift spaces. A coded shift space is defined as the 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 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). We also discuss flexibility results for the entropy on the concatenation and residual sets. Next, we present 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, Climenhaga and Thompson, and Pavlov. Finally, if time permits, we discuss the computability (in the sense of computable analysis) of measures of maximal entropy for coded shift spaces. The results presented in this talk are joint work with Tamara Kucherenko and Martin Schmoll.