A renormalization approach to irrational rotations

被引：2
|
作者：
Bonanno, Claudio [2 ]
Isola, Stefano [1 ]
机构：
[1] Univ Camerino, Dipartimento Matemat & Informat, I-62032 Camerino, Italy
[2] Univ Pisa, Dipartimento Matemat Applicata, I-56127 Pisa, Italy
来源：
ANNALI DI MATEMATICA PURA ED APPLICATA | 2009年 / 188卷 / 02期
关键词：
Irrational rotations; Continued fractions; Renormalization; Diffusion; RECURRENCE; TIME;
D O I：
10.1007/s10231-008-0074-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We introduce a renormalization procedure which allows us to study in a unified and concise way different properties of the irrational rotations on the unit circle beta bar right arrow {alpha + beta}, alpha is an element of R\Q. In particular, we obtain sharp results for the diffusion of the walk on Z generated by the location of points of the sequence {n alpha + beta} on a binary partition of the unit interval. Finally, we give some applications of our method.
引用
收藏
页码：247 / 267
页数：21
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