%0 Journal Article
%T Entropy of a semigroup of maps from a set-valued view
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Hou, B.
%A Wang, X.
%D 1999
%\ 11/30/1999
%V 43
%N 6
%P 1821-1835
%! Entropy of a semigroup of maps from a set-valued view
%K Topological entropy
%K semigroups
%K entropy-like invariants
%K Hausdorff metric
%R
%X 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.
%U http://bims.iranjournals.ir/article_1067_479aa58a4bb53422d87b5956ff62afe4.pdf