Stem and topological entropy on Cayley trees

  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={Mathematical Physics, Analysis and Geometry},
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… 
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