Chebyshev polynomials on generalized Julia sets

Date
2016
Authors
Alpan, G.
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Source Title
Computational Methods and Function Theory
Print ISSN
1617-9447
Electronic ISSN
2195-3724
Publisher
Springer
Volume
16
Issue
3
Pages
387 - 393
Language
English
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Abstract

Let (fn)n=1∞ be a sequence of non-linear polynomials satisfying some mild conditions. Furthermore, let Fm(z) : = (fm∘ fm - 1⋯ ∘ f1) (z) and ρm be the leading coefficient of Fm. It is shown that on the Julia set J(fn), the Chebyshev polynomial of degree deg Fm is of the form Fm(z) / ρm- τm for all m∈ N where τm∈ C. This generalizes the result obtained for autonomous Julia sets in Kamo and Borodin (Mosc. Univ. Math. Bull. 49:44–45, 1994). © 2015, Springer-Verlag Berlin Heidelberg.

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