On the Bernoulli property for rational maps
- 1 March 1985
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 5 (1), 71-88
- https://doi.org/10.1017/s0143385700002765
Abstract
Every rational function ƒ with degree has a unique invariant probability ƒƒ that maximizes entropy. It has been conjectured that the system (ƒ, μƒ) is equivalent to the one sided Bernoulli shift . In this paper we prove that there exists m >0 such that (ƒm, ƒƒ) is equivalent to .Keywords
This publication has 5 references indexed in Scilit:
- Entropy properties of rational endomorphisms of the Riemann sphereErgodic Theory and Dynamical Systems, 1983
- An invariant measure for rational mapsBulletin of the Brazilian Mathematical Society, New Series, 1983
- On the uniqueness of the maximizing measure for rational mapsBulletin of the Brazilian Mathematical Society, New Series, 1983
- Factors of Bernoulli shifts are Bernoulli shiftsAdvances in Mathematics, 1970
- Invariant sets under iteration of rational functionsArkiv för Matematik, 1965