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Random iterations of rational functions

Published online by Cambridge University Press:  19 September 2008

John Erik Fornaess  and
Nessim Sibony
John Erik Fornaess
Affiliation:
Princeton University, Princeton NJ 08540, USA
Nessim Sibony
Affiliation:
Université de Paris-Sud, Mathématique Bâtiment 425, 91405 Orsay Cedex, France
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Abstract

We study the asymptotic behavior of iterates of rational functions with small perturbations. In presence of attractive cycles we show that almost surely, in the parameter space, the iterates converge to a given neighborhood of the attractive cycles. When there is no attractive cycle, we prove an ergodic theorem with respect to Lebesgue measure.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 4 , December 1991 , pp. 687 - 708
Copyright
Copyright © Cambridge University Press 1991

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