Stable intersections of regular Cantor sets with large Hausdorff dimensions

Abstract

In this paper we prove a conjecture of J. Palis according to which the arithmetic difference of generic pairs of regular Cantor sets on the line either has zero Lebesgue measure or contains an interval. More precisely, we prove that if the sum of the Hausdorff dimensions of two regular Cantor sets is bigger than one, in almost all cases, there are translations of them whose intersection persistently has Hausdorff dimensions.

DOI: 10.2307/3062110

Authors

Carloa Gustavo T. de A. Moreira

Jean-Christophe Yoccoz