One-sided almost specification and intrinsic ergodicity
One-sided almost specification and intrinsic ergodicity
复制标题
片面的几乎规范和内在的遍历性
DOI：
10.1017/etds.2017.135
复制
发表时间：
2016
影响因子：
0.9
通讯作者：
R. Pavlov
中科院分区：
文献类型：
--
作者：
V. Climenhaga;R. Pavlov
我们定义了一种新的性质，称为单侧几乎规格性，它介于规格性和几乎规格性这两种性质之间，并证明了如果相应的误差函数\(g\)是有界的，它能保证内在遍历性（即最大熵测度的唯一性）。我们还表明，对于无界的\(g\)，例如\(\log\log n\)，唯一性可能不成立。我们的结果对几乎规格性有影响：我们证明了\(g\equiv1\)的几乎规格性蕴含单侧几乎规格性（\(g\equiv1\)），从而蕴含唯一性。另一方面，第二作者最近表明\(g\equiv4\)的几乎规格性并不蕴含唯一性。
We define a new property called one-sided almost specification, which lies between the properties of specification and almost specification, and prove that it guarantees intrinsic ergodicity (i.e. uniqueness of the measure of maximal entropy) if the corresponding mistake function $g$ is bounded. We also show that uniqueness may fail for unbounded $g$ such as $\log \log n$ . Our results have consequences for almost specification: we prove that almost specification with $g\equiv 1$ implies one-sided almost specification (with $g\equiv 1$ ) and hence uniqueness. On the other hand, the second author showed recently that almost specification with $g\equiv 4$ does not imply uniqueness.