Mathematika

Research Article

On the Lipschitz equivalence of Cantor sets

Dr. K. J. Falconera1 and Dr. D. T. Marsha2

a1 School of Mathematics, University of Bristol, University Walk, Bristol. BS8 1TW

a2 School of Mathematics, University of Bristol, University Walk, Bristol. BS8 1TW

Abstract

We show that under certain circumstances quasi self-similar fractals of equal Hausdorff dimensions that are homeomorphic to Cantor sets are equivalent under Hölder 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.

(Received May 16 1991)

Key Words:

  • 28A99: MEASURE AND INTEGRATION; Classical measure theory; Hausdorff measures.