Tail invariant measures of the Dyck shift

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish
Pages (from-to)61-83
Number of pages23
JournalIsrael Journal of Mathematics
Volume163
DOIs
StatePublished - 1 Jan 2008
Externally publishedYes

Fingerprint

Dive into the research topics of 'Tail invariant measures of the Dyck shift'. Together they form a unique fingerprint.

Cite this