Topology Proceedings 30 No. 1 (2006), pp. 265-278

Smooth Julia Sets of Elliptic Functions for Square Rhombic Lattices

Jane Hawkins

We discuss the dynamics of iterating the Weierstrass elliptic ℘ function with period lattice any real rhombic square lattice in C, that is a lattice generated by the complex numbers a + a i and a - a i, a > 0. We conjecture that the Julia set of ℘ for each such lattice is the whole sphere and describe a holomorphic family of these maps. We prove the conjecture in a specific case and give results supporting it in general.

Keywords: complex dynamics, Julia sets, meromorphic functions

Mathematics Subject Classification: 54H20 37F10 (37F20)

Document formats: PDF file 225.9 Kb

Topology Proceedings, Volume 30, No. 1 (2006)
Subscription information