Publication Date:
2000-01-01
Description:
We prove that there are families of rational maps of the sphere of degreen2(n=2,3,4,…)and2n2(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.
Print ISSN:
0161-1712
Electronic ISSN:
1687-0425
Topics:
Mathematics
Permalink