CHEBYSHEV POLYNOMIALS ON JULIA SETS AND EQUIPOTENTIAL CURVES FOR THE FAMILY P(z)=zd-c

被引：0

作者：

Xiao, Yingqing ^{[1
]}

Qiu, Weiyuan ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2009年 / 86卷 / 02期

关键词：

Chebyshev polynomials; Julia set; equipotential curve;

D O I：

10.1017/S1446788708000098

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that the d(n)th Chebyshev polynomials oil the Julia set J(P), and on the equipotential curve Gamma(P)(R), of the polynomial P(z) = z(d) - c, are identical and exactly equal to the nth iteration of P(z) itself. As an application, the capacity of the Julia set J(P) is deduced, a result that was first obtained by Brolin.

引用

页码：279 / 287

页数：9

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