Tail Invariant Measures of the Dyck Shift

Details Tail Invariant Measures of the Dyck Shift Tail Invariant Measures of the Dyck Shift

2004-06-02

arxiv.org/abs/math/0406045v3

Mathematics

Dynamical Systems

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 th

Scientific paper

We show that the one-sided Dyck shift has a unique tail invariant topologically $\sigma$-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.

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