Julia集和等势线上的Chebyshev多项式

肖映青, 邱维元

数学学报 ›› 2010, Vol. 53 ›› Issue (2) : 323-328.

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数学学报 ›› 2010, Vol. 53 ›› Issue (2) : 323-328. DOI: 10.12386/A2010sxxb0039
论文

Julia集和等势线上的Chebyshev多项式

    肖映青1, 邱维元2
作者信息 +

Chebyshev Polynomials on Julia Set and Equipotential Curves

    Ying Qing XIAO1, Wei Yuan QIU2
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文章历史 +

摘要

P表示一个度为d的首一多项式, JP表示它的Julia集.本文得到Julia集JP和其等势线ΓP(R)上的dn-阶Chebyshev多项式, 并举例说明二者并不总是相等.

 

Abstract

Let P be a monic polynomial of degree d, and JP be the Julia set of P. We obtain the dn-th Chebyshev polynomials on the Julia set JP and on the equipotential curves ΓP(R) of JP, and give an example to show that they are not always equal.

 

关键词

Julia集 / Chebyshev多项式 / 等势线

Key words

Julia set / Chebyshev polynomial / equipotential curves

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导出引用
肖映青, 邱维元. Julia集和等势线上的Chebyshev多项式. 数学学报, 2010, 53(2): 323-328 https://doi.org/10.12386/A2010sxxb0039
Ying Qing XIAO, Wei Yuan QIU. Chebyshev Polynomials on Julia Set and Equipotential Curves. Acta Mathematica Sinica, Chinese Series, 2010, 53(2): 323-328 https://doi.org/10.12386/A2010sxxb0039

参考文献


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[6] Fischer B., Chebyshev polynomials for disjoint compact sets, Constructive Approximation, 1992, 8: 309--329.

[7] Stawiska M., Chebyshev polynomials on equipotential curves of a quadratic Julia set, Univ. Iagell. Acta. Math., 1996, 33: 191--198.

[8] Beardon A.F., Iteration of Rational Functions, Berlin, New York: Springer-Verlag, 1991.

[9] Milnor J., Dynamics in One Complex Variable, Introductory Lectures, Braunschweig: Vieweg, 1999.

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基金

国家自然科学基金资助项目(10831004,10871047)

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