Arcwise connectedness of the set of ergodic measures of hereditary shifts
| Autor: | Jakub Konieczny, Dominik Kwietniak, Michal Kupsa |
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| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Mathematics::Dynamical Systems Social connectedness Applied Mathematics General Mathematics Dynamical Systems (math.DS) Interval (mathematics) Topological entropy Shift space Binary entropy function 37B10 37A05 37A25 37A30 37A35 37A45 37C40 Metric (mathematics) FOS: Mathematics Ergodic theory Mathematics - Dynamical Systems Invariant (mathematics) Mathematics |
| Zdroj: | Proceedings of the American Mathematical Society. 146:3425-3438 |
| ISSN: | 1088-6826 0002-9939 |
| DOI: | 10.1090/proc/14029 |
| Popis: | We show that the set of ergodic invariant measures of a shift space with a safe symbol (this includes all hereditary shifts) is arcwise connected when endowed with the $d$-bar metric. As a consequence the set of ergodic measures of such a shift is also arcwise connected in the weak-star topology and the entropy function over this set attains all values in the interval between zero and the topological entropy of the shift (inclusive). The latter result is motivated by a conjecture of A.~Katok. 13 pages. In the new version we have updated references and improved slightly the main result |
| Databáze: | OpenAIRE |
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