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Porosity of self-affine sets

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Abstract

In this paper, it is proved that any self-affine set satisfying the strong separation condition is uniformly porous. The author constructs a self-affine set which is not porous, although the open set condition holds. Besides, the author also gives a C 1 iterated function system such that its invariant set is not porous.

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Authors and Affiliations

  1. Institute of Mathematics, Zhejiang Wanli University, Ningbo, 315100, Zhejiang, China

    Lifeng Xi

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  1. Lifeng Xi
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Correspondence to Lifeng Xi.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 10671180, 10301029, 10241003).

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Xi, L. Porosity of self-affine sets. Chin. Ann. Math. Ser. B 29, 333–340 (2008). https://doi.org/10.1007/s11401-006-0422-y

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  • DOI: https://doi.org/10.1007/s11401-006-0422-y

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