Elliptic Functions with Disconnected Julia Sets
International Journal of Bifurcation and Chaos
In this paper, we investigate elliptic functions of the form , where is the Weierstrass elliptic function on a real rhombic lattice. We show that a typical function in this family has a superattracting fixed point at the origin and five other equivalence classes of critical points. We investigate conditions on the lattice which guarantee that has a double toral band, and we show that this family contains the first known examples of elliptic functions for which the Julia set is disconnected but not Cantor.
Koss, Lorelei. "Elliptic Functions with Disconnected Julia Sets." International Journal of Bifurcation and Chaos 26, no. 6 (2016): 10 pages. doi: 10.1142/S0218127416500954