Title
A Fundamental Dichotomy for Julia Sets of a Family of Elliptic Functions
Document Type
Article
Publication Date
11-2009
Department
Mathematics
Language
English
Publication Title
Proceedings of the American Mathematical Society
Abstract
We investigate topological properties of Julia sets of iterated elliptic functions of the form g = 1/p, where P is the Weierstrass elliptic function, on triangular lattices. These functions can be parametrized by 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.
DOI
10.1090/S0002-9939-09-09967-5
Recommended Citation
Comments
Published as:
Koss, Lorelei. "A Fundamental Dichotomy for Julia Sets of a Family of Elliptic Functions." Proceedings of the American Mathematical Society, 137 no. 11 (2009): 3927-3938.
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