# Random continued fractions

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Charlene Kalle

created by daniele on 11 Nov 2015

17 nov 2015
-- 15:00

Sala Conferenze, Collegio Puteano, CRM, Pisa

Seminari di Sistemi Dinamici Olomorfi, Pisa

**Abstract.**

We introduce a random dynamical system that produces for almost all points in the interval -1,1 uncountably many different continued fraction expansions. This system basically consists of random combinations of two well known continued fraction maps, namely the Gauss map and the backwards continued fraction map. We show that the random system has an invariant measure of a specific form and we identify some of its properties.