ON THE LIPSCHITZ EQUIVALENCE OF CANTOR SETS

被引：96

作者：

FALCONER, KJ

MARSH, DT

机构：

[1] University of Bristol, School of Mathematics, University Walk

来源：

MATHEMATIKA | 1992年 / 39卷 / 78期

关键词：

D O I：

10.1112/S0025579300014959

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that under certain circumstances quasi self-similar fractals of equal Hausdorff dimensions that are homeomorphic to Cantor sets are equivalent under Holder bijections of exponents arbitrarily close to 1. By setting up algebraic invariants for strictly self-similar sets, we show that such sets are not, in general, equivalent under Lipschitz bijections.

引用

页码：223 / 233

页数：11