Effective Equidistribution for Contact Anosov flows in Dimension Three

TL;DR

This paper proves that for contact Anosov flows on three-dimensional manifolds, the distribution of periodic orbits becomes uniform exponentially fast, providing effective rates of equidistribution.

Contribution

It establishes the first effective equidistribution results with exponential rates for contact Anosov flows in dimension three.

Findings

Bowen packets equidistribute exponentially fast

Effective rates of convergence for periodic orbit distributions

Application to contact Anosov flows in three dimensions

Abstract

We prove effective equidistribution theorems for (weighted) packets of closed periodic orbits for Anosov flows. In particular, for the case of contact Anosov flows on three-dimensional manifolds, we show that the Bowen packets equidistribute at an exponential rate.