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One-sided Lebesgue Bernoulli maps of the sphere of degree n 2 and 2n 2

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  • Julia A. Barnes
  • Lorelei Koss

Abstract

We prove that there are families of rational maps of the sphere of degree n 2 ( n = 2 , 3 , 4 , … ) and 2 n 2 ( 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.

Suggested Citation

  • Julia A. Barnes & Lorelei Koss, 2000. "One-sided Lebesgue Bernoulli maps of the sphere of degree n 2 and 2n 2," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 23, pages 1-10, January.
    • Handle: RePEc:hin:jijmms:619647
    DOI: 10.1155/S0161171200001484
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