IRREGULAR SETS, THE β-TRANSFORMATION AND THE ALMOST SPECIFICATION PROPERTY

被引：98

作者：

Thompson, Daniel J. ^{[1
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2012年 / 364卷 / 10期

基金：

英国工程与自然科学研究理事会;

关键词：

TOPOLOGICAL-ENTROPY; VARIATIONAL PRINCIPLE; MULTIFRACTAL ANALYSIS; DIVERGENCE POINTS; PRESSURE;

D O I：

10.1090/S0002-9947-2012-05540-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (X, d) be a compact metric space, f : X -> X be a continuous map satisfying a property we call almost specification (which is slightly weaker than the g-almost product property of Pfister and Sullivan), and phi : X -> R be a continuous function. We show that the set of points for which the Birkhoff average of phi does not exist (which we call the irregular set) is either empty or has full topological entropy. Every beta-shift satisfies almost specification and we show that the irregular set for any beta-shift or beta-transformation is either empty or has full topological entropy and Hausdorff dimension.

引用

页码：5395 / 5414

页数：20

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