Affiliation:
1. School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, P. R. China
Abstract
Self-similarity and Lipschitz equivalence are two basic and important properties of fractal sets. In this paper, we consider those properties of the union of Cantor set and its translate. We give a necessary and sufficient condition that the union is a self-similar set. Moreover, we show that the union satisfies the strong separation condition if it is of the self-similarity. By using the augment tree, we characterize the Lipschitz equivalence between Cantor set and the union of Cantor set and its translate.
Funder
NSFC
Research and Innovation Initiatives of WHPU
the China Scholarship Council
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Geometry and Topology,Modelling and Simulation