DYNAMICS OF A HIGHER DIMENSIONAL ANALOG OF THE TRIGONOMETRIC FUNCTIONS

被引：8

作者：

Bergweiler, Walter ^{[1
]}

Eremenko, Alexandre ^{[2
]}

机构：

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

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA | 2011年 / 36卷 / 01期

关键词：

Dynamics of entire functions; quasiregular map; Zorich map; Julia set; escaping set; Devaney hair; Hausdorff dimension; HAUSDORFF DIMENSION; FINITE-ORDER; ENTIRE MAPS; JULIA SETS; HAIRS; PARADOX; POINTS; AREA;

D O I：

10.5186/aasfm.2011.3610

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a quasiregular analog F of the sine and cosine function such that, for a sufficiently large constant lambda, the map x bar right arrow lambda F(x) is locally expanding. We show that the dynamics of this map define a representation of R-d, d >= 2, as a union of simple curves gamma: [0, infinity) -> R-d which tend to infinity and whose interiors gamma* = gamma((0, infinity)) are disjoint such that the union of all gamma* has Hausdorff dimension 1.

引用

页码：165 / 175

页数：11

共 25 条

[1]

[Anonymous], 1993, QUASIREGULAR MAPPING

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