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The dimensions of the divergence points of self-similar measures with weak separation condition

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Abstract

Let \(\mu \) be the self-similar measure supported on the self-similar set K with the weak separation condition, which is weaker than the open set condition. This article uses Hausdorff dimension and packing dimension to investigate the multifractal structure of several sets of divergence points of \(\mu \) in the iterated function system.

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Acknowledgments

We would like to thank Professors L. Olsen and S. Winter for sharing their papers with us. The first author was supported by NNSF of China (11601235), NSF of the Jiangsu Higher Education Institutions of China (16KJD110003), NSF of Jiangsu Province (BK20161014) and China Postdoctoral Science Foundation (2016M591873). The second author were supported by NNSF of China (11671208 and 11431012).

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Authors and Affiliations

  1. School of Mathematical Science, Nanjing Normal University, Nanjing, 210023, Jiangsu, People’s Republic of China

    Xiaoyao Zhou & Ercai Chen

  2. Center of Nonlinear Science, Nanjing University, Nanjing, 210093, Jiangsu, People’s Republic of China

    Ercai Chen

Authors
  1. Xiaoyao Zhou
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  2. Ercai Chen
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Correspondence to Ercai Chen.

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Communicated by J. Schoißengeier.

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Zhou, X., Chen, E. The dimensions of the divergence points of self-similar measures with weak separation condition. Monatsh Math 183, 379–391 (2017). https://doi.org/10.1007/s00605-016-1000-3

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  • DOI: https://doi.org/10.1007/s00605-016-1000-3

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