On shrinking targets for piecewise expanding interval maps

被引：20

作者：

Persson, Tomas ^{[1
]}

Rams, Michal ^{[2
]}

机构：

[1] Lund Univ, Ctr Math Sci, Box 118, S-22100 Lund, Sweden

[2] Polish Acad Sci, Inst Matematyczny, Ul Sniadeckich 8, PL-00656 Warsaw, Poland

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2017年 / 37卷

关键词：

D O I：

10.1017/etds.2015.49

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a map T : [0, 1] -> [0, 1] with an invariant measure mu, we study, for a mu-typical x, the set of points y such that the inequality vertical bar T-n x - y vertical bar < r(n) is satisfied for infinitely many n. We give a formula for the Hausdorff dimension of this set, under the assumption that T is piecewise expanding and mu(phi) is a Gibbs measure. In some cases we also show that the set has a large intersection property.

引用

页码：646 / 663

页数：18

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