Topological entropy of Markov set-valued functions
Topological entropy of Markov set-valued functions
复制标题
马尔可夫集值函数的拓扑熵
DOI：
10.1017/etds.2019.61
复制
发表时间：
2021
影响因子：
0.9
通讯作者：
James P. Kelly
中科院分区：
文献类型：
--
作者：
Lori Alvin;James P. Kelly
本文研究了一类上半连续集值函数的熵，称为马尔可夫集值函数，它是单值马尔可夫区间函数的推广。众所周知，马尔可夫区间函数的熵可以通过计算有限类型的相关移位的熵来找到。本文对马氏集值函数构造了一个类似的有限型移位，并利用这个移位空间求出了集值函数熵的上下界。
We investigate the entropy for a class of upper semi-continuous set-valued functions, called Markov set-valued functions, that are a generalization of single-valued Markov interval functions. It is known that the entropy of a Markov interval function can be found by calculating the entropy of an associated shift of finite type. In this paper, we construct a similar shift of finite type for Markov set-valued functions and use this shift space to find upper and lower bounds on the entropy of the set-valued function.