Uniform perfectness of self-affine sets
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- by Feng Xie, Yongcheng Yin and Yeshun Sun PDF
- Proc. Amer. Math. Soc. 131 (2003), 3053-3057 Request permission
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.References
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Additional Information
- Feng Xie
- Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, People’s Republic of China
- Address at time of publication: 420 Temple St., #517, New Haven, Connecticut 06511
- Email: xiefengmath@hotmail.com, feng.xie@yale.edu
- Yongcheng Yin
- Affiliation: 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
- Email: yin@math.zju.edu.cn
- Yeshun Sun
- Affiliation: Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, People’s Republic of China
- Email: sun@math.zju.edu.cn
- Received by editor(s): February 24, 2002
- Published electronically: April 30, 2003
- Additional Notes: This research was supported by the National Natural Science Foundation of China, Project No. 10171090.
- Communicated by: Michael Handel
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3053-3057
- MSC (2000): Primary 28A78, 28A80
- DOI: https://doi.org/10.1090/S0002-9939-03-06976-4
- MathSciNet review: 1993212