期刊论文

Feng, De-Jun

英文

Advances in Mathematics

0001-8708

2015

281

857-885

10.1016/j.aim.2015.06.002

The authors would like to thank Ranran Huang and Ying Xiong for helpful comments. The first author was partially supported by RGC grants in the Hong Kong Special Administrative Region, China (projects CUHK401112 , C UHK401013 ). The second author was partially supported by NSFC Nos. 11171128 , 11431007 , and 11471075 . The third author was supported in part by the AFOSR grant FA9550-12-1-0455 and NSF grant IIS-1302285 .

本校为其他机构

In this paper, we study the following question raised by Mattila in 1998: what are the self-similar subsets of the middle-third Cantor set C? We give criteria for a complete classification of all such subsets. We show that for any self-similar subset F of C containing more than one point, every linear generating IFS of F must consist of similitudes with contraction ratios ±3-n, n ∈N. In particular, a simple criterion is formulated to characterize self-similar subsets of C wit...