Dimensions of slowly escaping sets and annular itineraries for exponential functions

被引：2
|
作者：
Sixsmith, D. J. [1 ]
机构：
[1] Open Univ, Dept Math & Stat, Walton Hall, Milton Keynes MK7 6AA, Bucks, England
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2016年 / 36卷
基金：
英国工程与自然科学研究理事会;
关键词：
HAUSDORFF DIMENSION; JULIA SETS; POINTS; DYNAMICS; FAMILY; HAIRS; AREA;
D O I：
10.1017/etds.2015.7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the iteration of functions in the exponential family. We construct a number of sets, consisting of points which escape to infinity 'slowly', and which have Hausdorff dimension equal to 1. We prove these results by using the idea of an annular itinerary. In the case of a general transcendental entire function we show that one of these sets, the uniformly slowly escaping set, has strong dynamical properties and we give a necessary and sufficient condition for this set to be non-empty.
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页码：2273 / 2292
页数：20
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