학술논문
Lipschitz equivalence of self-similar sets satisfying the open set condition.
Document Type
Journal Translation
Author
Xiong, Ying (PRC-SCT) AMS Author Profile; Xi, Li Feng (PRC-ZWU-IM) AMS Author Profile
Source
Subject
28 Measure and integration -- 28A Classical measure theory
28A80Fractals
28A80
Language
Chinese
Abstract
Given $r\in(0,1)$ and $N\ge2$, let $E$ and $E'$ be self-similar setsgenerated by $N$ similitudes in the forms $S(x)=\pm rx+b$. Suppose thatthe two self-similar sets $E$ and $E'$ satisfy the open set condition (OSC)and that the open setin the OSC can be chosen as an open interval. Thispaper proves that under such conditions $E$ and $E'$ are Lipschitz equivalent.This is arotation version of the $\{1,3,5\}$-$\{1,4,5\}$ problem proposed by G. David andS.~W. Semmes [{\it Fractured fractals and broken dreams},Oxford Lecture Ser. Math. Appl., 7, Oxford Univ. Press, New York, 1997; MR1616732 (99h:28018)].