Examples of Parametrized Families of Elliptic Functions with Empty Fatou Sets

Lorelei Koss, Dickinson College

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Abstract

In this paper, we investigate parametrized families of elliptic functions on real rectangular lattices. Although these functions have at most four critical values, we prove that they have at most one attracting or parabolic cycle of Fatou components. We find some families for which the Julia set is always the entire sphere.