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}
}
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
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