New York Journal of Mathematics
Volume 20 (2014) 607-625


Lorelei Koss

Examples of parametrized families of elliptic functions with empty Fatou sets

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Published: June 20, 2014
Keywords: Complex dynamics, meromorphic functions, Julia sets
Subject: Primary 54H20, 37F10; Secondary 37F20

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.

Author information

Department of Mathematics and Computer Science, Dickinson College, P.O. Box 1773, Carlisle, PA 17013