Double-Tail Invariant Measures of the Dyck Shift

2004/08/15 by Tom Meyerovitch, Meyerovitch, Tom
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS

paper · pdf · doi:10.48550/arxiv.math/0408201

arxiv created 2004/08/15 · arxiv updated 2009/12/01

Abstract

In a previous paper by the author, it was shown that the One sided Dyck is uniquely ergodic with respect to the one sided-tail relation, where the tail invariant probability is also shift invariant and obtains the topological entropy. In this paper 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. We also prove that this probability, along with the two equilibrium probabilities of the Dyck shift are the only ergodic double-tail invariant probabilities for the Dyck shift.

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