Stem and topological entropy on Cayley trees
Dynamical Systems
2022-01-05 v1
Abstract
We consider the existence of the topological entropy of shift spaces on a finitely generated semigroup whose Cayley graph is a tree. The considered semigroups include free groups. On the other hand, the notion of stem entropy is introduced. For shift spaces on a strict free semigroup, the stem entropy coincides with the topological entropy. We reveal a sufficient condition for the existence of the stem entropy of shift spaces on a semigroup. Furthermore, we demonstrate that the topological entropy exists in many cases and is identical to the stem entropy.
Cite
@article{arxiv.2110.08960,
title = {Stem and topological entropy on Cayley trees},
author = {Jung-Chao Ban and Chih-Hung Chang and Yu-Liang Wu and Yu-Ying Wu},
journal= {arXiv preprint arXiv:2110.08960},
year = {2022}
}