# Random iteration on hyperbolic Riemann surfaces – Marco Abate (University of Pisa)

CRM – SNS.

#### Abstract

In this talk we shall describe the asymptotic behaviour of sequences of functions obtained by iteratively left-composing or right-composing holomorphic self-maps of a hyperbolic Riemann surface $X$. We shall consider in detail two cases: when the holomorphic self-maps to be composed have values in a Bloch subdomain of~$X$; and when the holomorphic self-maps to be composed are sufficiently close to a given self-map. This is a joint work with Argyrios Christodoulou.

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