A Julia Set That Is Everything
Let ℘ be the Weierstrass ℘-function. Then ℘(2z)=R(℘(z)) for some rational function R· It was shown by Lattès (1919) that the Julia set of this rational function R is the whole sphere. A similar example using Jacobian elliptic functions had been considered before by Böttcher. The purpose of this paper is to explain the underlying idea of this example, and its relevance in dynamics. The necessary background material from dynamics and elliptic functions is included, so that the paper is accessible to nonexperts and, in particular, students.