David Simmons

Random Iteration of Rational Functions David Simmons

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 Urba?ski ('91) concerning existence and uniqueness of equilibrium states of rational functions with respect to Hölder continuous potential functions satisfying a "pressure gap" condition. The main results also generalize a theorem of Jonsson ('00).