On Mixing Flows on Finite Area Translation Surfaces

TL;DR

This paper constructs explicit examples of infinite-genus translation surfaces with finite area where the vertical flow exhibits strong mixing, answering a previously open question in the field.

Contribution

It introduces a new family of translation surfaces with strong mixing properties, advancing understanding of dynamical behaviors on such surfaces.

Findings

Constructed explicit finite-area, infinite-genus translation surfaces

Demonstrated strong mixing in vertical translation flow on these surfaces

Provided a positive answer to an open question by Lindsey and Treviño

Abstract

We construct an explicit family of finite-area, infinite-genus translation surfaces whose vertical translation flow is strongly mixing. This provides a positive answer to a question posed by Lindsey and Trevi\~no~\cite{LT}