Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): L. Koss
Journal: Proc. Amer. Math. Soc. 137 (2009), 3927-3938.
MSC (2000): Primary 54H20, 37F10; Secondary 37F20
Posted: June 29, 2009
MathSciNet review: 2529903
Retrieve article in: PDF

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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 is either Cantor or connected, and we obtain examples of each type.

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