Induced dynamics on the hyperspaces
Submitted: 2015-10-09
|Accepted: 2016-07-12
|Published: 2016-10-03
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Keywords:
hyperspace, combined dynamics, relations, induced map, transitivity, super-transitivity, dense periodicity
Supporting agencies:
Abstract:
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.
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