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arXiv · 2110.08960

Stem and topological entropy on Cayley trees

Jung-Chao Ban·Chih-Hung Chang·Yu-Liang Wu·Yu-Ying Wu
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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.

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Jung-Chao Ban, Chih-Hung Chang, Yu-Liang Wu, Yu-Ying Wu. 2021-10-18. Stem and topological entropy on Cayley trees. https://doi.org/10.1007/s11040-021-09411-4

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