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Uniform perfectness of self-affine sets |
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| Authors: | Feng Xie Yongcheng Yin Yeshun Sun |
| Affiliation: | 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  be affine maps of Euclidean space  with each  nonsingular and each  contractive. We prove that the self-affine set  of  is uniformly perfect if it is not a singleton. |
| Keywords: | Uniformly perfect set self-affine set Hausdorff dimension |
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