Dynamical properties of the derivative of the Weierstrass elliptic function

Goldsmith, Jeff; Koss, Lorelei

doi:10.2140/involve.2009.2.267

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Dynamical properties of the derivative of the Weierstrass elliptic function

Jeff Goldsmith and Lorelei Koss

Vol. 2 (2009), No. 3, 267–288

DOI: 10.2140/involve.2009.2.267

Abstract

We discuss properties of the Julia and Fatou sets of the derivative of the Weierstrass elliptic $℘$ function. We find triangular lattices for which the Julia set is the whole sphere, or which have superattracting fixed or period two points. We study the parameter space of the derivative of the Weierstrass elliptic function on triangular lattices and explain the symmetries of that space.

Keywords

complex dynamics, meromorphic functions, Julia sets

Mathematical Subject Classification 2000

Primary: 30D99, 37F10, 37F45

Milestones

Received: 31 July 2008

Accepted: 29 March 2009

Published: 3 October 2009

Communicated by Gaven J. Martin

Authors

Jeff Goldsmith
Johns Hopkins Department of Biostatistics 615 N. Wolfe Street E3037 Baltimore, MD 21205 United States

Lorelei Koss
Department of Mathematics and Computer Science Dickinson College P.O. Box 1773 Carlisle, PA 17013 United States

Vol. 2, No. 3, 2009