Tail invariant measures of the Dyck shift |
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Authors: | Tom Meyerovitch |
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Institution: | (1) School of mathematical sciences, Tel Aviv University, 69978 Tel Aviv, Israel |
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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.
This article is a part of the author’s M.Sc. Thesis, written under the supervision of J. Aaronson, Tel-Aviv University. |
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