Random Iteration of Rational Functions
Simmons David
Random Iteration of Rational Functions
Simmons David
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The goal of this book is to study the ergodic theory of holomorphic random dynamical systems on the Riemann sphere. Specifically, the main results are two generalizations of a theorem of Denker and Urbanski (‘91) concerning existence and uniqueness of equilibrium states of rational functions with respect to Hoelder continuous potential functions satisfying a pressure gap condition. The main results also generalize a theorem of Jonsson ('00).
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