HAUSDORFF DIMENSIONS OF THE JULIA SETS OF RELUCTANTLY RECURRENT RATIONAL MAPS

被引：0

作者：

Li, Huaibin ^{[1
,2
]}

机构：

[1] Henan Univ, Sch Math & Informat Sci, Kaifeng 475004, Henan Province, Peoples R China

[2] Pontificia Univ Catolica Chile, Fac Matemat, Santiago, Chile

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2013年 / 44卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Rational maps; Julia sets; Hausdorff dimension; hyperbolic dimension;

D O I：

10.1007/s13226-013-0046-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider a rational map f of degree at least two acting on Riemman sphere (C) over cap that is expanding away from critical points. Assuming that all critical points of f in the Julia set J(f) are reluctantly recurrent, we prove that the Hausdorff dimension of the Julia set J(f) is equal to the hyperbolic dimension, and the Lebesgue measure of Julia set is zero when the Julia set J(f) not equal (C) over cap.

引用

页码：849 / 863

页数：15

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