ARCWISE CONNECTEDNESS OF THE SET OF ERGODIC MEASURES OF HEREDITARY SHIFTS

作者：Konieczny Jakub^*; Kupsa Michal; Kwietniak Dominik

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2018, 146(8): 3425-3438.

DOI：10.1090/proc/14029

• Kolmogorov-Sinai (metric) entropy
• hereditary shift space
• Poulsen simplex
• Besicovitch pseudometric
• d-bar metric

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.

• 出版日期2018-8