Induced dynamics on the hyperspaces

Puneet Sharma

doi:10.4995/agt.2016.4154

Authors

Puneet Sharma Indian Institute of Technology Jodhpur

DOI:

https://doi.org/10.4995/agt.2016.4154

Keywords:

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

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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Author Biography

Puneet Sharma, Indian Institute of Technology Jodhpur

Department of Mathematics

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