论文标题
诱导转化的均匀正熵
Uniformly Positive Entropy of Induced Transformations
论文作者
论文摘要
令$（x，t）$为一个拓扑动力系统，由紧凑的度量空间$ x $和连续的弹跳图$ t：x \ to x $组成。通过使用局部熵理论，我们证明$（x，t）$在诱导的系统$（\ cm（x），\ wt {t}）$的情况下具有均匀的积极熵，这是在与弱$^*$ topology赋予的Borel概率度量上的。该结果可以看作是由于格拉斯纳和魏斯而导致的拓扑熵的相应结果均匀正熵概念的版本。
Let $(X,T)$ be a topological dynamical system consisting of a compact metric space $X$ and a continuous surjective map $T : X \to X$. By using local entropy theory, we prove that $(X,T)$ has uniformly positive entropy if and only if so does the induced system $(\cM(X),\wt{T})$ on the space of Borel probability measures endowed with the weak$^*$ topology. This result can be seen as a version for the notion of uniformly positive entropy of the corresponding result for topological entropy due to Glasner and Weiss.
