Induced dynamics on the hyperspaces

Puneet Sharma


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.


hyperspace; combined dynamics; relations; induced map; transitivity; super-transitivity; dense periodicity

Subject classification

37B20; 37B99; 54C60; 54H20

Full Text:



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Information and Computation  vol: 274  first page: 104532  year: 2020  
doi: 10.1016/j.ic.2020.104532

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