Characteristic measures for language stable subshifts
Abstract
We consider the problem of when a symbolic dynamical system supports a Borel probability measure that is invariant under every element of its automorphism group. It follows readily from a classical result of Parry that the full shift on finitely many symbols, and more generally any mixing subshift of finite type, supports such a measure. Frisch and Tamuz recently dubbed such measures characteristic, and further showed that every zero entropy subshift has a characteristic measure. While it remains open if every subshift over a finite alphabet has a characteristic measure, we define a new class of shifts, which we call language stable subshifts, and show that these shifts have characteristic measures. This is a large class that is generic in several senses and contains numerous positive entropy examples.
Cite
@article{arxiv.2101.12669,
title = {Characteristic measures for language stable subshifts},
author = {Van Cyr and Bryna Kra},
journal= {arXiv preprint arXiv:2101.12669},
year = {2021}
}