On the arithmetic sum of regular Cantor sets

被引：10
|
作者：
Palis, J [1 ]
Yoccoz, JC [1 ]
机构：
[1] UNIV PARIS 11,DEPT MATH,ORSAY,FRANCE
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 1997年 / 14卷 / 04期
关键词：
D O I：
10.1016/S0294-1449(97)80135-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove here that for any pair of regular Canter sets in the line, either its arithmetic sum has Lebesgue measure zero or the pair can be approximated (through the image of a smooth diffeomorphism) by another one whose arithmetic sum contains an interval. The latter occurs when the Hausdorff dimension of the product of the sets is bigger than one.
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页码：439 / 456
页数：18
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