Entropy of a semigroup of maps from a set-valued view Article Swipe
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Bingzhe Hou
,
Xu Wang
·
YOU?
·
· 2016
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1601.03294
· OA: W2238895987
YOU?
·
· 2016
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.1601.03294
· OA: W2238895987
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 Biś. 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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