Abstract

In this paper, we investigate elliptic functions of the form [Formula: see text], where [Formula: see text] 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 [Formula: see text] 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.

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