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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 2

Hypercyclic operators for iterated function systems

Mohammad Salman(University of Delhi)0000-0002-7835-8446
Ruchi Das(University of Delhi)0000-0002-1889-9988
Pages
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Publication Date
2021-04-11
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we introduce and study the notion of hypercyclicity for iterated function systems (IFS) of operators.
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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.

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Cite This Article

Salman, M., Das, R. (2021). Hypercyclic operators for iterated function systems. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 2. https://doi.org/10.15672/hujms.716686

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