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Local Dimensions and Quantization Dimensions in Dynamical Systems

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Abstract

Let \(\mu \) be a Borel probability measure generated by a hyperbolic recurrent iterated function system defined on a nonempty compact subset of \(\mathbb R^k\). We study the Hausdorff and the packing dimensions, and the quantization dimensions of \(\mu \) with respect to the geometric mean error. The results establish the connections with various dimensions of the measure \(\mu \) and generalize many known results about local dimensions and quantization dimensions of measures.

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Acknowledgements

The authors are grateful to the referees for their valuable comments and suggestions.

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Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, 1201 West University Drive, Edinburg, TX, 78539-2999, USA

    Mrinal Kanti Roychowdhury

  2. Analysis, Probability & Fractals Laboratory: LR18ES17, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, 5000, Monastir, Tunisia

    Bilel Selmi

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  1. Mrinal Kanti Roychowdhury
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  2. Bilel Selmi
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Correspondence to Bilel Selmi.

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Roychowdhury, M.K., Selmi, B. Local Dimensions and Quantization Dimensions in Dynamical Systems. J Geom Anal 31, 6387–6409 (2021). https://doi.org/10.1007/s12220-020-00537-5

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