Dynamical properties of the derivative of the Weierstrass elliptic function

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.