## Uniqueness of the measure of maximal entropy for the squarefree flow

### Time

Nov 15 2012 – 3:00pm – 3:50 pm

### Location

MW154

### Speaker

Ryan Peckner (Princeton)

### Abstract

The squarefree flow is a natural dynamical system whose topological and ergodic properties are closely linked to the behavior of squarefree numbers. We prove that the squarefree flow carries a unique measure of maximal entropy and describe the structure of the associated measure-preserving dynamical system. Our method involves first studying approximations arising from finite collections of prime numbers, then taking a limit under Ornstein’s dˉ-metric in order to consider all primes simultaneously. This is accomplished by proving uniform Gibbs bounds for a sequence of sofic systems and constructing explicit joinings between them in order to directly estimate their dˉ-distances.