KARPINSKA'S PARADOX IN DIMENSION 3

被引：17

作者：

Bergweiler, Walter ^{[1
]}

机构：

[1] Univ Kiel, D-24098 Kiel, Germany

来源：

DUKE MATHEMATICAL JOURNAL | 2010年 / 154卷 / 03期

关键词：

LAMBDA-EXP Z; HAUSDORFF DIMENSION; EXPONENTIAL MAPS; FINITE-ORDER; JULIA SETS; DYNAMICS; POINTS; MAPPINGS; HAIRS; BASINS;

D O I：

10.1215/00127094-2010-047

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It was proved by Devaney and Krych, by McMullen, and by Karpinska that, for 0 < lambda < 1/e, the Julia set of lambda e(z) is an uncountable union of pairwise disjoint simple curves tending to infinity, and the Hausdorlf dimension of this set is 2, but the set of curves without endpoints has Hausdorff dimension 1. We show that these results have 3-dimensional analogues when the exponential function is replaced by a quasi-regular self-map of R(3) introduced by Zorich.

引用

页码：599 / 630

页数：32

共 41 条

[1] Trees and hairs for some hyperbolic entire maps of finite order [J].