Document Type

Article

Publication Date

2000

Department

Mathematics

Language

English

Publication Title

International Journal of Mathematics and Mathematical Sciences

Abstract

We prove that there are families of rational maps of the sphere of degree n2 (n = 2,3,4,...) and 2n2 (n = 1,2,3,...) which, with respect to a finite invariant measure equivalent to the surface area measure, are isomorphic to one-sided Bernoulli shifts of maximal entropy. The maps in question were constructed by Böettcher (1903–1904) and independently by Lattès (1919). They were the first examples of maps with Julia set equal to the whole sphere.

Comments

This published version is made available on Dickinson Scholar with the permission of the publisher. For more information on the published version, visit Hindawi Publishing Corporation's Website.

DOI

10.1155/S0161171200001484

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Mathematics Commons

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