Entropy of a semigroup of maps from a set-valued view

Document Type : Research Paper


College of Mathematics‎, ‎Jilin university‎, ‎130012‎, ‎Changchun‎, ‎P‎. ‎R‎. ‎China.


In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreover, some notions of chaos are also well generalized for finitely generated semigroups from a set-valued view.


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