Arithmetic density

TL;DR

This paper investigates the density properties of arithmetic classes, which are special subsets of Euclidean space defined by arithmetical conditions relevant to dynamical systems, using advanced mathematical techniques.

Contribution

It provides new density estimates for arithmetic classes by applying Dani-Kleinbock-Margulis methods, extending understanding of their structure in Euclidean space.

Findings

Established density bounds for arithmetic classes.

Applied Dani-Kleinbock-Margulis techniques to new settings.

Enhanced understanding of arithmetical conditions in dynamical systems.

Abstract

Arithmetic class are closed subsets of the euclidean space which generalise arithmetical conditions encoutered in dynamical systems, such as diophantine conditions or Bruno type conditions. I prove density estimates for such sets using Dani-Kleinbock-Margulis techniques.