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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: L. Koss
Journal: Proc. Amer. Math. Soc. 137 (2009), 3927-3938
MSC (2000): Primary 54H20, 37F10; Secondary 37F20
Published electronically: June 29, 2009
MathSciNet review: 2529903
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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 $ g$ is either Cantor or connected, and we obtain examples of each type.


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Additional Information

L. Koss
Affiliation: Department of Mathematics and Computer Science, Dickinson College, P.O. Box 1773, Carlisle, Pennsylvania 17013
Email: koss@dickinson.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09967-5
PII: S 0002-9939(09)09967-5
Keywords: Complex dynamics, meromorphic functions, Julia sets
Received by editor(s): January 21, 2009
Received by editor(s) in revised form: March 3, 2009
Published electronically: June 29, 2009
Communicated by: Jane M. Hawkins
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.