# Random iteration on hyperbolic Riemann surfaces

@inproceedings{Abate2021RandomIO, title={Random iteration on hyperbolic Riemann surfaces}, author={Marco Abate and Argyrios Christodoulou}, year={2021} }

Let {fν} ⊂ Hol(X,X) be a sequence of holomorphic self-maps of a hyperbolic Riemann surface X. In this paper we shall study the asymptotic behavior of the sequences obtained by iteratively left-composing or rightcomposing the maps {fν}; the sequences of self-maps of X so obtained are called left (respectively, right) iterated function systems. We shall obtain the analogue for left iterated function systems of the theorems proved by Beardon, Carne, Minda and Ng for right iterated function systems… Expand

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