标题：One-sided Lebesgue Bernoulli maps of the sphere
of degree <mml:math alttext="$n^2$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math> and <mml:math alttext="$2n^2$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>2</mml:mn><mml:msup><mml:mi>n</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math>
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2000
卷号：23
DOI：10.1155/S0161171200001484
出版社：Hindawi Publishing Corporation
摘要：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.
