One-sided Lebesgue Bernoulli maps of the sphere of degree n 2 and 2n 2

Julia A. Barnes and Lorelei Koss

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-10

Abstract:

We prove that there are families of rational maps of the sphere of degree n 2 ( n = 2 , 3 , 4 , … ) and 2 n 2 ( 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.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:619647

DOI: 10.1155/S0161171200001484

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