2021/01/11 by Burkart, Jack, Lazebnik, Kirill · 1 citation
#30D05 #30D30 #37F10 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.2101.04219
Let (Mj)j=1^∞∈ℕ and (rj)j=1^∞∈ℝ+ be increasing sequences satisfying some mild rate of growth conditions. We prove that there is an entire function f: ℂ →ℂ whose behavior in the large annuli \ z∈ℂ : rj⋅exp(π/Mj)≤|z|≤ rj+1\ is given by a perturbed rescaling of z↦ zMj, such that the only singular values of f are rescalings of ± rjMj. We describe several applications to the dynamics of entire functions.