Communications in Mathematical Physics

, Volume 181, Issue 3, pp 733–739 | Cite as

Large deviations and the distribution of pre-images of rational maps

  • Mark Pollicott
  • Richard Sharp


In this article we prove a large deviation result for the pre-images of a point in the Julia set of a rational mapping of the Riemann sphere. As a corollary, we deduce a convergence result for certain weighted averages of orbital measures, generalizing a result of Lyubich.


Neural Network Statistical Physic Weighted Average Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Mark Pollicott
    • 1
  • Richard Sharp
    • 1
  1. 1.Department of MathematicsUniversity of ManchesterManchesterUK

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