Residual generic ergodicity of periodic group extensions over translation surfaces

TL;DR

This paper demonstrates that in each stratum of translation surfaces, a residual set exists where geodesic flows in almost every direction are ergodic for most periodic group extensions created via a cutting technique.

Contribution

It establishes residual generic ergodicity of periodic group extensions over translation surfaces, extending previous work to a broader class of surfaces.

Findings

Residual set of surfaces with ergodic geodesic flows in almost every direction.

Ergodicity holds for almost-every periodic group extension using cuts.

Extends ergodic properties to all strata of translation surfaces.

Abstract

Continuing the work in \cite{ergodic-infinite}, we show that within each stratum of translation surfaces, there is a residual set of surfaces for which the geodesic flow in almost every direction is ergodic for almost-every periodic group extension produced using a technique referred to as \emph{cuts}.