- Hacettepe Journal of Mathematics and Statistics
- Vol: 50 Issue: 2
- Hypercyclic operators for iterated function systems
Hypercyclic operators for iterated function systems
Authors : Mohammad Salman, Ruchi Das
Pages : 483-491
Doi:10.15672/hujms.716686
View : 12 | Download : 6
Publication Date : 2021-04-11
Article Type : Research
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