Hypercyclic operators for iterated function systems

Key Findings & Data: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.

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Conclusion & Impact:We also give some equivalent conditions for hypercyclicity as well as weakly mixing for an IFS of operators.

🔬Design:Research Article

📍Scope:Comprehensive Sample

⚙️Variables:Iterated function systems · hypercyclic operators · sensitive operators

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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Cite This Article

Salman, M., Das, R. (2022). Hypercyclic operators for iterated function systems. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 2, 483–491. https://ajindex.com/articles/529548

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