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Conformal Geometry and Dynamics

ISSN 1088-4173

 
 

 

Parametrized dynamics of the Weierstrass elliptic function


Authors: Jane Hawkins and Lorelei Koss
Translated by:
Journal: Conform. Geom. Dyn. 8 (2004), 1-35
MSC (2000): Primary 37F45
DOI: https://doi.org/10.1090/S1088-4173-04-00103-1
Published electronically: February 24, 2004
MathSciNet review: 2060376
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Abstract: We study parametrized dynamics of the Weierstrass elliptic $\wp$ function by looking at the underlying lattices; that is, we study parametrized families $\wp_{\Lambda}$ and let $\Lambda$ vary. Each lattice shape is represented by a point $\tau$ in a fundamental period in modular space; for a fixed lattice shape $\Lambda = [1, \tau]$ we study the parametrized space $k \Lambda$. We show that within each shape space there is a wide variety of dynamical behavior, and we conduct a deeper study into certain lattice shapes such as triangular and square. We also use the invariant pair $(g_2, g_3)$ to parametrize some lattices.


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Additional Information

Jane Hawkins
Affiliation: Department of Mathematics, University of North Carolina at Chapel Hill, CB #3250, Chapel Hill, North Carolina 27599-3250
Email: jmh@math.unc.edu

Lorelei 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/S1088-4173-04-00103-1
Keywords: Complex dynamics, meromorphic functions, Julia sets, holomorphic families, parameter space
Received by editor(s): May 21, 2003
Received by editor(s) in revised form: January 23, 2004
Published electronically: February 24, 2004
Additional Notes: The second author was supported in part by NSF Grant 9970575
Article copyright: © Copyright 2004 American Mathematical Society

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