Tamara Kucherenko
The City University of New York (CUNY)
Title
Entropy Maximizing Measures for Coded Shifts: Beyond Uniqueness
Abstract
Many dynamical systems admit a distinguished probability measure that captures their statistical behavior, known as the measure of maximal entropy. For classical symbolic systems, such as shifts of finite type and sofic shifts, this measure is unique, but this fails for more general systems called coded shifts. While non-uniqueness is often viewed as pathological, it is still possible to obtain a detailed description of entropy maximizing measures in this setting. In this talk, we show that, under natural conditions, an ergodic measure of maximal entropy can be associated with a generator for which it is Bernoulli, yielding a unified perspective on both uniqueness and non-uniqueness phenomena.