Dimensional characteristics of invariant measures for circle diffeomorphisms

被引：7

作者：

Sadovskaya, Victoria ^{[1
]}

机构：

[1] Univ S Alabama, Dept Math & Stat, Mobile, AL 36688 USA

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2009年 / 29卷

关键词：

D O I：

10.1017/S0143385708000916

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider pointwise, box, and Hausdorff dimensions of invariant measures for circle diffeomorphisms. We discuss the cases of rational, Diophantine, and Lionville rotation numbers. Our main result is that for any Lionville number tau there exists a C(infinity) circle diffeomorphism with rotation number tau such that the pointwise and box dimensions of its unique invariant measure do not exist. Moreover, the lower pointwise and lower box dimensions can equal any value 0 <= beta <= 1.

引用

页码：1979 / 1992

页数：14

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