Proof of a folklore Julia set connectedness theorem and connections with elliptic functions

Abstract

Abstract. We prove the following theorem about Julia sets of the maps This is related to connectivity results by the author and others about J(℘), where ℘ denotes the Weierstrass elliptic ℘ function, especially where the period lattice has some symmetry. We illustrate several further connections between the dynamics of some specific elliptic functions and the family f n,p,γ for some values of n and p.