A FUNDAMENTAL DICHOTOMY FOR JULIA SETS OF A FAMILY OF ELLIPTIC FUNCTIONS

被引：3

作者：

Koss, L. ^{[1
]}

机构：

[1] Dickinson Coll, Dept Math & Comp Sci, Carlisle, PA 17013 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 137卷 / 11期

关键词：

Complex dynamics; meromorphic functions; Julia sets; MEROMORPHIC FUNCTIONS; ITERATION;

D O I：

10.1090/S0002-9939-09-09967-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate topological properties of Julia sets of iterated elliptic functions of the form g = 1/p, where p is the Weierstrass elliptic function, on triangular lattices. These functions can be parametrized by C - {0}, and they all have a superattracting fixed point at zero and three other distinct critical values. We prove that the Julia set of g is either Cantor or connected, and we obtain examples of each type.

引用

页码：3927 / 3938

页数：12

共 24 条

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