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Random iterations of rational functions

  • John Erik Fornaess (a1) and Nessim Sibony (a2)


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.



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Random iterations of rational functions

  • John Erik Fornaess (a1) and Nessim Sibony (a2)


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