One-sided Lebesgue Bernoulli maps of the sphere of degree \(n^2\) and \(2n^2\)
type: Item
instance of: scholarly article
title: One-sided Lebesgue Bernoulli maps of the sphere of degree \(n^2\) and \(2n^2\)
zbMATH Open document ID: 0984.37050
DOI: 10.1155/S0161171200001484
author: Julia A. Barnes
author: Lorelei Koss
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2000-11-06T00:00:00Z
full work available at URL: https://eudml.org/doc/49156
review text: This paper is devoted to a class of rational maps of the sphere whose Julia set is the whole sphere. More precisely, the authors examine two families of rational maps which were constructed by Böttcher and Latties and construct direct isomorphisms between these families of maps and one-sided Bernoulli shifts with respect to the maximal entropy measure. The athors show that, for the maps under considerations the maximal entropy measure is equivalent to the surface area measure.
Mathematics Subject Classification ID: 37F50
Mathematics Subject Classification ID: 37F10
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 28D99
zbMATH DE Number: 1488483
zbMATH Keywords: Julia set
zbMATH Keywords: Bernoulli map
zbMATH Keywords: maximal entropy measure
zbMATH Keywords: surface area measure
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1488483