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.
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Communicated by Ya. G. Sinai
The first author was supported by a Royal Society University Fellowship during part of this research.
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Pollicott, M., Sharp, R. Large deviations and the distribution of pre-images of rational maps. Commun.Math. Phys. 181, 733–739 (1996). https://doi.org/10.1007/BF02101295
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DOI: https://doi.org/10.1007/BF02101295