Hypercyclic operators for iterated function systems

Year 2021, Volume: 50 Issue: 2, 483 - 491, 11.04.2021

Mohammad Salman , Ruchi Das

https://doi.org/10.15672/hujms.716686

Abstract

In this paper we introduce and study the notion of hypercyclicity for iterated function systems (IFS) of operators. We prove that for a linear IFS, hypercyclicity implies sensitivity and if an IFS is abelian, then hypercyclicity also implies multi-sensitivity and hence thick sensitivity. We also give some equivalent conditions for hypercyclicity as well as weakly mixing for an IFS of operators.

Keywords

Iterated function systems, hypercyclic operators, sensitive operators, weakly mixing operators

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