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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
Article

Abstract

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.

Keywords

Neural Network Statistical Physic Weighted Average Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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