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.

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.

For more information on the published version, visit American Mathematical Society's Website.

DOI

10.1090/S0002-9939-09-09967-5

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