Induced dynamics on the hyperspaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 03 Oct 2016Embargo end date: 01 Dec 2015 Spain Publisher:Universitat Politecnica de ValenciaJournal:Applied General Topology, volume 17, page 93 (issn: 1576-9402, eissn: 1989-4147,

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Authors: Sharma, Puneet;

doi: 10.4995/agt.2016.4154 , 10.48550/arxiv.1512.06940

arXiv: 1512.06940

Induced dynamics on the hyperspaces

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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>

Country

Spain

Related Organizations

Universitat Politècnica de València
Spain
Indian Institute of Technology BHU
India
Indian Institute of Technology Jodhpur
India

Keywords

Dynamical Systems (math.DS), Topological dynamics, Combined dynamics, 37B20, 37B99, 54C60, 54H20, QA1-939, FOS: Mathematics, Super-transitivity, Mathematics - Dynamical Systems, transitivity, Dense periodicity, Relations, Set-valued maps in general topology, QA299.6-433, Transitivity, combined dynamics, super-transitivity, Hyperspace, Induced map, relations, dense periodicity., induced map, hyperspace, Notions of recurrence and recurrent behavior in topological dynamical systems, dense periodicity, Mathematics, Analysis

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