Factor maps of collective dynamics and hyperspace entropy
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Submission date: 29. Jun. 2020
MSC-Numbers: 37B40, 37C15, 54B20, 54H20, 60B40
Keywords and phrases: Hyperspace, Topological dynamics, Topological entropy
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Given a topological dynamical system, we consider its induced collective dynamics on the space of probability measures with the weak topology and on the hyperspace of closed subsets with the lower Vietoris topology. We show that the support of measures is a factor map between these collective dynamics, and that the topological entropy of the induced hyperspace system equals the entropy of the base system.