Title
A Julia Set That Is Everything
Document Type
Article
Publication Date
10-2003
Department
Mathematics
Language
English
Publication Title
Mathematics Magazine
Abstract
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.
Recommended Citation
Comments
Published as:
Barnes, Julia and Lorelei Koss. "A Julia Set That Is Everything." Mathematics Magazine 76, no. 4 (2003): 255-63.
For more information on the published version, visit Mathematical Association of America's Website.