New York Journal of Mathematics
Volume 24 (2018), 947-979


Jane Hawkins and Mónica Moreno Rocha

Dynamics and Julia sets of iterated elliptic functions

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Published: October 14, 2018.
Keywords: complex dynamics, Julia sets, meromorphic functions, elliptic functions.
Subject: 37F10, 32A20, 30D05.

We study the parametrized family of elliptic functions of the form FΛ,b(z)=℘Λ(z)+b for b∈ C, Λ a lattice, and ℘Λ the Weierstrass elliptic ℘ function with period lattice Λ. We show that the dynamics depend on b as b varies within one fundamental region of C/Λ, and on the lattice Λ. We analyze properties of the Julia sets, and bifurcations of FΛ,b, focussing on real rectangular lattices; in particular the dynamical properties are more diverse than those coming from the family ℘Λ with Λ varying.


Author information

Jane Hawkins:
Department of Mathematics
University of North Carolina at Chapel Hill
Chapel Hill, NC 27599, USA.


Mónica Moreno Rocha:
Centro de Investigación en Matemáticas
A.P. 402, C.P. 36240
Guanajuato, Gto., México.