Arcwise connectedness of the set of ergodic measures of hereditary shifts
Arcwise connectedness of the set of ergodic measures of hereditary shifts
复制标题
遗传转变的遍历测度集的弧向连通性
DOI：
10.1090/proc/14029
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Dominik Kwietniak
中科院分区：
文献类型：
--
作者：
Jakub Konieczny;M. Kupsa;Dominik Kwietniak
我们证明，当赋予 $d$-bar 度量时，具有安全符号的移位空间（这包括所有遗传移位）的遍历不变测度集是弧向连接的。因此，这种位移的遍历测度集也在弱星形拓扑中弧向连接，并且该集合上的熵函数获得零和位移的拓扑熵（含）之间的区间内的所有值。后一个结果是由 A.~Katok 的猜想激发的。
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.