Speed of Weak Mixing for the Chacon Map

TL;DR

This paper investigates the rate of weak mixing for the Chacon map by analyzing spectral properties of related subshifts and establishing bounds that are nearly optimal.

Contribution

It introduces spectral estimates for a class of subshifts conjugate to the Chacon map and derives sharp bounds on the speed of weak mixing for the map.

Findings

Spectral estimates for a conjugate subshift of the Chacon map

Derived bounds on the speed of weak mixing for the Chacon map

Established the bounds are essentially sharp

Abstract

We first consider a non-primitive substitution subshift that is conjugate to the Chacon map. We then derive spectral estimates for a particular subshift and the speed of weak mixing for a class of observables with certain regularity conditions. After, we use these results to find the speed of weak mixing for the Chacon map on the interval and show that this bound is essentially sharp.