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Transitivity and sensitivity of iterated function systems via Furstenberg families

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Abstract

In this paper, we study variants of transitivity and sensitivity via Furstenberg families for iterated function systems (IFSs). Using the concept of skew product transformation of an IFS, we obtain results related to characterizations of the concepts studied. Also results regarding the inverse, conjugacy and product of IFSs are studied. Wherever necessary examples and counterexamples are provided related to the results obtained.

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Acknowledgements

Authors are thankful to the referees for their valuable comments and suggestions for improvement of the paper. The first author is supported by CSIR-SRF Sr.No. 1121641416 Ref.No: 18/12/2016(ii) EU-V (File No: 09/045(1532)/2017-EMR-I) for carrying out this research work.

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  1. Department of Mathematics, University of Delhi, Delhi, 110007, India

    Rahul Thakur & Ruchi Das

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  1. Rahul Thakur
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  2. Ruchi Das
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Correspondence to Ruchi Das.

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Thakur, R., Das, R. Transitivity and sensitivity of iterated function systems via Furstenberg families. Aequat. Math. 94, 1123–1140 (2020). https://doi.org/10.1007/s00010-020-00757-8

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  • DOI: https://doi.org/10.1007/s00010-020-00757-8

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