# A simultaneous version of Host's equidistribution Theorem

## Dynamical Systems Seminar

## Meeting Details

For more information about this meeting, contact Kristin Berrigan, Svetlana Katok, Kurt Vinhage.

**Speaker:** Amir Algom, Penn State

**Abstract:** Let q,m>1 be coprime integers. In 1995 Host proved that if P is a times q invariant ergodic measure with positive entropy, then P almost every x is normal to base m. This result , which is closely related to Furstenberg's times 2, times 3 Conjecture, was later extended by Lindenstrauss to the case when q does not divide any power of m. Recently, Hochman and Shmerkin showed that it holds in the "correct" generality, i.e. assuming only that q and m are independent. We further extend this result, showing that for P typical x the orbit of (x,x) under the diagonal toral endomorphism (times q, times m) equidistributes for the product measure of P with the Lebesgue measure.

## Room Reservation Information

**Room Number:** 114 McAllister

**Date:** 09/23/2019

**Time:** 3:40pm - 4:40pm