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 Hölder continuous potential functions satisfying a "pressure gap" condition. The main results also generalize a theorem of Jonsson ('00).

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Produktbeschreibung
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 Hölder continuous potential functions satisfying a "pressure gap" condition. The main results also generalize a theorem of Jonsson ('00).
Autorenporträt
David Simmons is a retired Fellow of the Royal Collage of Anaesthetists with 30 years experience in anaesthesia and pain management in the UK, South Africa and Australia. He has also taught medicine at the University of Sydney, which has made him a brilliant educationalist not only to students and colleagues but also to the general public.