One-sided Lebesgue Bernoulli maps of the sphere of degree \(n^2\) and \(2n^2\) (Q1574351)

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.