Abstract
<p> </p><p>In this paper, we study the dynamics induced by finite commutative relation on the hyperspaces. We prove that the dynamics induced on the hyperspace by a non-trivial commutative family of continuous self maps cannot be transitive and hence cannot exhibit higher degrees of mixing. We also prove that the dynamics induced on the hyperspace by such a collection cannot have dense set of periodic points. We also give example to show that the induced dynamics in this case may or may not be sensitive.</p>
Publisher
Universitat Politecnica de Valencia
Cited by
2 articles.
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1. Dynamic to Quotients of Hyperspaces;Zurnal matematiceskoj fiziki, analiza, geometrii;2022-06-25
2. Topological dynamics of Nondeterministic Cellular Automata;Information and Computation;2020-10