A fundamental dichotomy for Julia sets of a family of elliptic functions

Koss, L.

doi:10.1090/S0002-9939-09-09967-5

A fundamental dichotomy for Julia sets of a family of elliptic functions
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Proc. Amer. Math. Soc. 137 (2009), 3927-3938 Request permission

Abstract:

We investigate topological properties of Julia sets of iterated elliptic functions of the form $g = 1/\wp$, where $\wp$ is the Weierstrass elliptic function, on triangular lattices. These functions can be parametrized by $\mathbb {C} - \{0\}$, and they all have a superattracting fixed point at zero and three other distinct critical values. We prove that the Julia set of $g$ is either Cantor or connected, and we obtain examples of each type.

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