Extender sets and measures of maximal entropy for subshifts
Dynamical Systems
2019-07-03 v2
Abstract
We prove inequalities relating the measures of maximal entropy of two patterns u,v where the extender set of u is contained in the extender set of v. Our main results are two generalizations of a Theorem of Meyerovitch; the first applies to all such v,w when G=Z, and the second to v,w with the same shape and any countable amenable finitely generated torsion-free G. As a consequence of our results we give new and simpler proofs of several facts about synchronizing subshifts and we answer a question of Climenhaga.
Keywords
Cite
@article{arxiv.1808.09486,
title = {Extender sets and measures of maximal entropy for subshifts},
author = {Felipe García-Ramos and Ronnie Pavlov},
journal= {arXiv preprint arXiv:1808.09486},
year = {2019}
}
Comments
accepted in the Journal of the London Mathematical Society