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 language | English |
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Pages (from-to) | 61-83 |
Number of pages | 23 |
Journal | Israel Journal of Mathematics |
Volume | 163 |
DOIs | |
State | Published - 1 Jan 2008 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics