Chebyshev polynomials on generalized Julia sets

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 $ρ_m$ 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 $F_m(z)/ρ_m-τ_m$ for all $m\in\mathbb{N}$ where $τ_m\in\mathbb{C}$. This generalizes the result obtained for autonomous Julia sets.

No reviews yet.

No comments yet.