# Ergodic Theory for Markov Fibred Systems and Parabolic Rational Maps

```@inproceedings{Aaronson2010ErgodicTF,
title={Ergodic Theory for Markov Fibred Systems and Parabolic Rational Maps},
author={Jon Aaronson and M. Denker and Mariusz Urbanski},
year={2010}
}```
• Published 2010
A parabolic rational map of the Riemann sphere admits a nonatomic /¡-conformai measure on its Julia set where h = the HausdorfT dimension of the Julia set and satisfies 1/2 < h < 2 . With respect to this measure the rational map is conservative, exact and there is an equivalent cr-finite invariant measure. Finiteness of the measure is characterised. Central limit theorems are proved in the case of a finite invariant measure and return sequences are identified in the case of an infinite one. A… CONTINUE READING
Highly Cited
This paper has 22 citations. REVIEW CITATIONS