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Tail Invariant Measures of the Dyck Shift

Tom Meyerovitch
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Abstract

We show that the one-sided Dyck shift has a unique tail invariant topologically $σ$-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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Tom Meyerovitch. 2007-11-07. Tail Invariant Measures of the Dyck Shift. https://arxiv.org/abs/math/0406045

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