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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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