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
收藏
页码：646 / 663
页数：18
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