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
DOI:
https://doi.org/10.1090/S0002-9939-09-09967-5
Published electronically:
June 29, 2009
MathSciNet review:
2529903
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: We investigate topological properties of Julia sets of iterated elliptic functions of the form , where
is the Weierstrass elliptic function, on triangular lattices. These functions can be parametrized by
, and they all have a superattracting fixed point at zero and three other distinct critical values. We prove that the Julia set of
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:
https://doi.org/10.1090/S0002-9939-09-09967-5
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.