Cantor Julia Sets in a Family of Even Elliptic Functions
Journal of Difference Equations and Applications
In this paper, we investigate topological properties of the Julia set of a family of even elliptic functions on real rectangular lattices. These functions have two real critical points and, depending on the shape of the lattice, one or two non-real critical points. We prove that if 0 is the only real fixed point then the Julia set is Cantor. We show that functions with Cantor Julia sets exist within every equivalence class of real rectangular lattices, and we generally locate the parameters giving rise to these Julia sets in the parameter plane representing real lattices.