Tail Invariant Measures of the Dyck Shift
Abstract
We show that the one-sided Dyck shift has a unique tail invariant topologically -finite measure (up to scaling). This invariant measure of the one sided Dyck turns out to be a shift-invariant probability. Furthermore, it is one of the two ergodic probabilities obtaining maximal entropy. For the two sided Dyck shift we show that there are exactly three ergodic double-tail invariant probabilities. We show that the two sided Dyck has a double-tail invariant probability, which is also shift invariant, with entropy strictly less than the topological entropy.
Cite
@article{arxiv.math/0406045,
title = {Tail Invariant Measures of the Dyck Shift},
author = {Tom Meyerovitch},
journal= {arXiv preprint arXiv:math/0406045},
year = {2007}
}
Comments
Replaces old version of this article and also of math.DS/0408201. To appear in Israel J. of Math. This article is a part of the author's M.Sc. thesis, written under the supervision of J. Aaronson, Tel-Aviv University