A fundamental dichotomy for Julia sets of a family of elliptic functions
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- by L. Koss
- Proc. Amer. Math. Soc. 137 (2009), 3927-3938
- DOI: https://doi.org/10.1090/S0002-9939-09-09967-5
- Published electronically: June 29, 2009
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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.References
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Bibliographic Information
- L. Koss
- Affiliation: Department of Mathematics and Computer Science, Dickinson College, P.O. Box 1773, Carlisle, Pennsylvania 17013
- MR Author ID: 662937
- Email: koss@dickinson.edu
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3927-3938
- MSC (2000): Primary 54H20, 37F10; Secondary 37F20
- DOI: https://doi.org/10.1090/S0002-9939-09-09967-5
- MathSciNet review: 2529903