Strong limit theorems for infinite measure-preserving dynamical systems with applications to non-standard continued fraction algorithms

by Dr Tanja Schindler (Univ. of Wien)

Thursday 16 Mar 2023, 15:00 → 16:00 Europe/Rome

CRM - SNS

Aaronson's theorem states that if we have a non-integrable observable over a finite measure system or if we have an integrable observable over a infinite measure space, then in both cases we can not have a strong law of large numbers. However - depending on the precise properties of the system - it is still possible to obtain almost sure convergence after a suitable truncation of the system (deleting maximal entries in the finite measure case and adding additional summands in the infinite measure case). In this talk we will look at a setting which can be seen as a combination of both situations: We have an infinite invariant measure and an observable which is non-integrable on a finite measure set. We will look at suitable truncations in this setting. Easy examples which fit exactly in our setting are the backwards and the even integer continued fractions. This is joint work with Claudio Bonanno.