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

Part of: Complex dynamical systems

Published online by Cambridge University Press:  01 April 2009

YINGQING XIAO  and
WEIYUAN QIU
YINGQING XIAO*
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China
WEIYUAN QIU
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China (email: wyqiu@fudan.edu.cn)
*
✉For correspondence; e-mail: xiaoyingqing@yahoo.com.cn
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Abstract

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It is shown that the dnth Chebyshev polynomials on the Julia set JP, and on the equipotential curve ΓP(R), of the polynomial P(z)=zd−c, are identical and exactly equal to the nth iteration of P(z) itself. As an application, the capacity of the Julia set JP is deduced, a result that was first obtained by Brolin.

Keywords

Chebyshev polynomialsJulia setequipotential curve

MSC classification

Secondary: 37F99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 2 , April 2009 , pp. 279 - 287
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This work is supported by NNSF No. 10571028.

References

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