## Dynamics, Geometry, & Groups - Marco Lenci (Universita di Bologna)

### Friday, August 23rd, 2019

**Time:** 10:30 a.m** Place:** Jeffery Hall 319

**Speaker:** Marco Lenci (Universita di Bologna)

**Title:** Infinite-volume mixing and the case of one-dimensional maps with an indifferent fixed point.

**Abstract:** I will first discuss the question of mixing in infinite ergodic theory, which will serve as a motivation for the introduction of the notions of "infinite-volume mixing". Then I will focus on a prototypical class of infinite-measure-preserving dynamical systems: non-uniformly expanding maps of the unit interval with an indifferent fixed point. I will show how the definitions of infinite-volume mixing play out in this case. As it turns out, the most significant property, and the hardest to verify, is the so-called global-local mixing, corresponding to the decorrelation in time between global and local observables. I will present sufficient conditions for global-local mixing, which will cover the most popular examples of maps with an indifferent fixed point (Pomeau-Manneville and Liverani-Saussol-Vaienti). If time permits, I will also present some peculiar limit theorems that can be derived for these systems out of the property of global-local mixing.