Abstract
Let \((f_n)_{n=1}^\infty \) be a sequence of non-linear polynomials satisfying some mild conditions. Furthermore, let \(F_m(z):=(f_m\circ f_{m-1}\cdots \circ f_1)(z)\) and \(\rho _m\) be the leading coefficient of \(F_m\). It is shown that on the Julia set \(J_{(f_n)}\), the Chebyshev polynomial of degree \(\deg {F_m}\) is of the form \(F_m(z)/\rho _m-\tau _m\) for all \(m\in \mathbb {N}\) where \(\tau _m\in \mathbb {C}\). This generalizes the result obtained for autonomous Julia sets in Kamo and Borodin (Mosc. Univ. Math. Bull. 49:44–45, 1994).
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Communicated by Vladimir V. Andrievskii.
The author is supported by a grant from Tübitak: 115F199.
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Alpan, G. Chebyshev Polynomials on Generalized Julia Sets. Comput. Methods Funct. Theory 16, 387–393 (2016). https://doi.org/10.1007/s40315-015-0145-8
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DOI: https://doi.org/10.1007/s40315-015-0145-8