Title

Parametrized Dynamics of the Weierstrass Elliptic Function

Document Type

Article

Publication Date

2-24-2004

Department

Mathematics

Language

English

Publication Title

Conformal Geometry & Dynamics

Abstract

We study parametrized dynamics of the Weierstrass elliptic ℘ function by looking at the underlying lattices; that is, we study parametrized families ℘Λ and let Λ vary. Each lattice shape is represented by a point τ in a fundamental period in modular space; for a fixed lattice shape Λ = [1, τ] we study the parametrized space kΛ. 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 (g2, g3) to parametrize some lattices.

Comments

Published as:
Hawkins, Jane and Lorelei Koss. "Parametrized Dynamics of the Weierstrass Elliptic Function." Conformal Geometry and Dynamics 8, no. 1 (2004): 1-35.

For more information on the published version, visit American Mathematical Society's Website.

DOI

10.1090/S1088-4173-04-00103-1

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