Fast and slow points of Birkhoff sums

被引：6

作者：

Bayart, Frederic ^{[1
,2
]}

Buczolich, Zoltan ^{[2
]}

Heurteaux, Yanick ^{[1
,2
]}

机构：

[1] Univ Clermont Auvergne, LMBP, UMR CNRS 6620, Campus Cezeaux,3 Pl Vasarely,TSA 60026,CS 60026, F-63178 Aubiere, France

[2] Eotvos Lorand Univ, Dept Anal, Pazmany Peter Setany 1-c, H-1117 Budapest, Hungary

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2020年 / 40卷 / 12期

关键词：

Birkhoff sum; typical; generic properties; group rotation; coboundary; law of iterated logarithm; SQUARE-ROOT; GIANT LEAP; RANDOMNESS;

D O I：

10.1017/etds.2019.45

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the growth rate of the Birkhoff sums S-n,S-alpha f(x) = Sigma(n-1)(k=0) f(x + k alpha) where f is a continuous function with zero mean defined on the unit circle T and (alpha, x) is a 'typical' element of T-2. The answer depends on the meaning given to the word 'typical'. Part of the work will be done in a more general context.

引用

页码：3236 / 3256

页数：21

共 20 条

[1]

[Anonymous], 1994, Princeton Mathematical Series

[2] RECURRENCE OF CO-CYCLES AND RANDOM-WALKS [J].