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The packing measure of a class of generalized sierpinski carpet

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Analysis in Theory and Applications

Abstract

For\(\frac{1}{4}< a< \frac{{\sqrt 2 }}{4}\), let S1(x)=ax, S2(x)=1−a+ax, x∈[0, 1]. Ca is the attractor of the iterated function system {S1, S2}, then the packing measure of Ca×Ca is Ps(a)(Ca×Ca)=4·2s(a)(1−a)s(a), wheres(a)=-log a 4.

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Authors and Affiliations

  1. Mathematics and Scientific Computer College, Zhongshan University, 510275, Guangzhou, P. R. China

    Jia Baoguo

  2. Mathematics Department, Zhaoqing University, 526061, Zhaoqing, Guangdong, P. R. China

    Zhu Zhiwei

Authors
  1. Jia Baoguo
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  2. Zhu Zhiwei
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Additional information

This project was supported in part by the Foundations of the Natural Science Committee, Guangdong Province and Zhongshan University Advanced Research Centre, China.

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Baoguo, J., Zhiwei, Z. The packing measure of a class of generalized sierpinski carpet. Anal. Theory Appl. 20, 69–76 (2004). https://doi.org/10.1007/BF02835260

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  • DOI: https://doi.org/10.1007/BF02835260

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