Cohomological equations for linear involutions

TL;DR

This paper extends existing results on cohomological equations from interval exchange transformations to a broader class called irreducible linear involutions, enhancing the theoretical understanding of these dynamical systems.

Contribution

It introduces new results for cohomological equations in the context of irreducible linear involutions, expanding the scope of prior work on interval exchange transformations.

Findings

Extended cohomological equation results to linear involutions

Broadened the class of transformations analyzed

Provided theoretical insights into dynamical systems

Abstract

In the current note we extend results by Marmi, Moussa and Yoccoz about cohomological equations for interval exchange transformations to irreducible linear involutions.