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Stable Intersections of Regular Cantor Sets with Large Hausdorff Dimensions

Carlos Gustavo T. de A. Moreira and Jean-Christophe Yoccoz
Annals of Mathematics
Second Series, Vol. 154, No. 1 (Jul., 2001), pp. 45-96
Published by: Annals of Mathematics
DOI: 10.2307/3062110
Stable URL: http://www.jstor.org/stable/3062110
Page Count: 52
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Stable Intersections of Regular Cantor Sets with Large Hausdorff Dimensions
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Abstract

In this paper we prove a conjecture by 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 then, in almost all cases, there are translations of them whose intersection persistently has Hausdorff dimension.

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