$\mathbb{Z}_+^k$-作用的方向原像熵

Directional Preimage Entropy for $\mathbb{Z}_+^k$-Actions

中文关键词:  $\mathbb{Z}_+^k$-作用  方向原像熵  无限图

英文关键词:$\mathbb{Z}_{+}^k$-actions  directional preimage entropy  infinite graph

中文摘要:

      本文提出了$\mathbb{Z}_+^k$-作用的方向原像熵的概念, 得到了关于这些熵之间的一些关系并证明了在拓扑共轭下的各类方向原像熵的不变性. 最后本文给出几类具有零分枝方向原像熵的系统: 由扩张映射生成的$\mathbb{Z} _{+}^k$-作用, 有限图及一类无限图上的 $\mathbb{Z}_{+}^k$-作用.

英文摘要:

      In this paper, a new type of entropy, directional preimage entropy including topological and measure theoretic versions for $\mathbb{Z}_{+}^k$-actions, is introduced. Some of their properties including relationships and the invariance are obtained. Moreover, several systems including $\mathbb{Z}_{+}^k$-actions generated by the expanding maps, $\mathbb{Z}_{+}^k$-actions defined on finite graphs and some infinite graphs with zero directional preimage branch entropy are studied.