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Trees with non-regular fractal boundary

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Abstract

For any given 0 < α < β < ∞, we construct a tree such that under tree metric, the Hausdorff dimension of the corresponding boundary is α, but both the Packing dimension and the boxing dimension are β. Applying the connection between tree and iterated functions system, nonregular fractal sets on real line are constructed. Moreover, the method adopted in our paper is different from those which have been used before for constructing non-regular fractal set in general metric space.

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Authors and Affiliations

  1. Department of Mathematics, School of Sciences, Wuhan University of Technology, Wuhan, 430070, P. R. China

    Jing Hu Yu

  2. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan, 430071, P. R. China

    Yi Ming Ding

Authors
  1. Jing Hu Yu
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  2. Yi Ming Ding
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Correspondence to Jing Hu Yu.

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This research is partially supported by the National Science Foundation of China

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Yu, J.H., Ding, Y.M. Trees with non-regular fractal boundary. Acta. Math. Sin.-English Ser. 24, 1345–1350 (2008). https://doi.org/10.1007/s10114-008-6261-x

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  • DOI: https://doi.org/10.1007/s10114-008-6261-x

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