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Uniform perfectness of self-affine sets
Authors:Feng Xie  Yongcheng Yin  Yeshun Sun
Institution:Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, People's Republic of China ; Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, People's Republic of China -- and -- Morningside Center of Mathematics, Chinese Academy of Sciences, Beijing 100080, People's Republic of China ; Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, People's Republic of China
Abstract:Let $f_i(x)=A_ix+b_i (1\le i\le n)$ be affine maps of Euclidean space $\mathbb{R} ^N$ with each $A_i$ nonsingular and each $f_i$ contractive. We prove that the self-affine set $K$ of $\{f_1,\dots, f_n\}$ is uniformly perfect if it is not a singleton.

Keywords:Uniformly perfect set  self-affine set  Hausdorff dimension
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