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Hausdorff and upper box dimension estimate of hyperbolic recurrent sets

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Abstract

In this paper, under the open set condition we have determined the lower and upper bounds of the Hausdorff dimensions and the upper box-counting dimensions of the limit sets of hyperbolic recurrent iterated function systems in terms of the unique zeros h and H of the two pressure functions. In addition, we have estimated the bounds of h, H-dimensional Hausdorff and packing measures. The result in this paper generalizes existing results about fractal dimensions of many other iterated function systems.

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Authors and Affiliations

  1. Department of Mathematics, The University of Texas-Pan American, 1201 West University Drive, Edinburg, TX, 78539-2999, USA

    Mrinal Kanti Roychowdhury

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  1. Mrinal Kanti Roychowdhury
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Correspondence to Mrinal Kanti Roychowdhury.

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Roychowdhury, M.K. Hausdorff and upper box dimension estimate of hyperbolic recurrent sets. Isr. J. Math. 201, 507–523 (2014). https://doi.org/10.1007/s11856-014-0028-0

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  • DOI: https://doi.org/10.1007/s11856-014-0028-0

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