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Dimensions of cookie-cutter-like sets

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Abstract

The cookie-cutter-like sets are defined as the limit sets of a sequence of classical cookie-cutter mappings. By introducing Gibbs-like measures, we study the dimensions, Hausdorff and packing measures of the CC-like sets, and then discuss the continuous dependence of the dimensions.

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Authors and Affiliations

  1. Laboratory of Pure and Applied Mathematics, Wuhan University, 430072, Wuhan, China

    Jihua Ma & Hui Rao

  2. Department of Mathematics, Tsinghua University, 100084, Beijing, China

    Zhiying Wen

Authors
  1. Jihua Ma
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  2. Hui Rao
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  3. Zhiying Wen
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Correspondence to Zhiying Wen.

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Ma, J., Rao, H. & Wen, Z. Dimensions of cookie-cutter-like sets. Sci. China Ser. A-Math. 44, 1400–1412 (2001). https://doi.org/10.1007/BF02877068

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  • DOI: https://doi.org/10.1007/BF02877068

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