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Chebyshev polynomials on generalized Julia sets (1504.08278v1)

Published 30 Apr 2015 in math.DS

Abstract: Let $(f_n){n=1}\infty$ be a sequence of nonlinear polynomials satisfying some mild conditions. Furthermore, let $F_m(z)=(f_m\circ f{m-1}\ldots \circ f_1)(z)$ and $\rho_m$ be the leading coefficient for $F_m$. It is shown that on the Julia set $J_{(f_n)}$, the Chebyshev polynomial of the 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.

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