Entropy of a semigroup of maps from a set-valued view
Dynamical Systems
2016-01-14 v1
Abstract
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 Bi\'s. 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.
Keywords
Cite
@article{arxiv.1601.03294,
title = {Entropy of a semigroup of maps from a set-valued view},
author = {Bingzhe Hou and Xu Wang},
journal= {arXiv preprint arXiv:1601.03294},
year = {2016}
}
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13 pages, 0 figures