Annales Academić Scientiarum Fennicć
Mathematica
Volumen 37, 2012, 229-243

LIPSCHITZ EQUIVALENCE OF A CLASS OF SELF-SIMILAR SETS WITH COMPLETE OVERLAPS

Qiuli Guo, Hao Li, Qin Wang and Lifeng Xi

Zhejiang Wanli University, Institute of Mathematics
Ningbo, Zhejiang, 315100, P.R. China; guoqiuli 'at' zwu.edu.cn

Zhejiang Wanli University, Institute of Mathematics
Ningbo, Zhejiang, 315100, P.R. China; kevinlee9809 'at' yahoo.com.cn

Zhejiang Wanli University, School of Computer Science and Information Technology
Ningbo, Zhejiang, 315100, P.R. China; qinwang 'at' 126.com

Zhejiang Wanli University, Institute of Mathematics
Ningbo, Zhejiang, 315100, P.R. China; xilifengningbo 'at' yahoo.com

Abstract. Fix r \in (0,1/3]. We discuss a class of self-similar sets {K_n}_{n \ge 1} with complete overlaps, where K_n = (rK_n) \cup (rK_n + rⁿ(1 - r)) \cup (rK_n + 1 - r). We prove that for any n₁, n₂ \ge 1, K_n1 and K_n2 are Lipschitz equivalent.

2010 Mathematics Subject Classification: Primary 28A80.

Key words: Fractals, self-similar set, Lipschitz equivalence, complete overlaps.

Reference to this article: Q. Guo, H. Li, Q. Wang and L. Xi: Lipschitz equivalence of a class of self-similar sets with complete overlaps. Ann. Acad. Sci. Fenn. Math. 37 (2012), 229-243.

Full document as PDF file

doi:10.5186/aasfm.2012.3712