International Journal of Mathematics and Mathematical Sciences
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.
Barnes, Julia A. and Lorelei Koss. "One-Sided Lebesgue Bernoulli Maps of the Sphere of Degree n² and 2n²." International Journal of Mathematics and Mathematical Sciences 23, no. 6 (2000): 383-92.