Title

A Julia Set That Is Everything

Authors

Julia Barnes
Lorelei Koss, Dickinson College

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.

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.

Recommended Citation