Applications of joinings to sparse equidistribution problems

TL;DR

This paper explores how the classification of joinings in dynamical systems can be applied to solve sparse equidistribution problems in homogeneous dynamics, providing quantitative estimates through recent results.

Contribution

It introduces a novel approach linking joinings classification with sparse equidistribution, offering new quantitative bounds in homogeneous dynamics.

Findings

Established a method to apply joinings classification to sparse equidistribution problems.

Derived quantitative estimates for equidistribution in homogeneous spaces.

Connected recent quantitative results to practical applications in dynamical systems.

Abstract

We show how classification of joinings of two dynamical systems can be used in some sparse equidistribution problems in homogeneous dynamics, and by using recent quantitative results about equidistribution theorems, one can deduce some quantitative estimates for such problems.