Ergodic theory for markov fibred systems and parabolic rational maps

Jon Aaronson, Manfred Denker, Mariusz Urbański

Research output: Contribution to journalArticle

132 Scopus citations

Abstract

A parabolic rational map of the Riemann sphere admits a nonatomic-conformai measure on its Julia set where h = the Hausdorff 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 σ-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 theory of Markov fibred systems is developed, and parabolic rational maps are considered within this framework.

Original languageEnglish (US)
Pages (from-to)495-548
Number of pages54
JournalTransactions of the American Mathematical Society
Volume337
Issue number2
DOIs
StatePublished - Jun 1993

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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