no code implementations • 17 Dec 2020 • Xiaobo Hou, Xueting Tian, Yiwei Zhang
Pfister and Sullivan proved that if a topological dynamical system $(X, T)$ satisfies almost product property and uniform separation property, then for each nonempty compact %convex subset $K$ of invariant measures, the entropy of saturated set $G_{K}$ satisfies \begin{equation}\label{Bowen's topological entropy} h_{top}^{B}(T, G_{K})=\inf\{h(T,\mu):\mu\in K\}, \end{equation} where $h_{top}^{B}(T, G_{K})$ is Bowen's topological entropy of $T$ on $G_{K}$, and $h(T,\mu)$ is the Kolmogorov-Sinai entropy of $\mu$.
Dynamical Systems 37C50, 37B20, 37B05, 37D45, 37C45
