Equidistribution and measure rigidity under $\times p,\times q$

TL;DR

This paper demonstrates that the equidistribution of irrational orbits on the unit circle leads to a proof of Furstenberg's conjecture, connecting dynamical systems and number theory.

Contribution

It establishes a new link between equidistribution properties and measure rigidity, providing a potential pathway to resolve Furstenberg's conjecture.

Findings

Equidistribution of irrational orbits implies Furstenberg's conjecture.

Connects measure rigidity with equidistribution on the unit circle.

Provides a new approach to longstanding conjecture in dynamics.

Abstract

We show that equidistribution of irrational orbits on the unit circle implies Furstenberg's conjecture.