H\"older regularity of the solutions of the cohomological equation for Roth type interval exchange maps

TL;DR

This paper proves that solutions to the cohomological equation for Roth type interval exchange maps are Hölder continuous under certain smoothness and subspace conditions, advancing understanding of regularity in dynamical systems.

Contribution

It establishes Hölder regularity of solutions for the cohomological equation in Roth type interval exchange maps with smooth data in specific subspaces.

Findings

Solutions are Hölder continuous for data of class C^r with r>1

Regularity holds under finite-codimension linear subspace conditions

Advances understanding of dynamical regularity in interval exchange maps

Abstract

We prove that the solutions of the cohomological equation for Roth type interval exchange maps are H\"older continuous provided that the datum is of class $C^r$ with $r>1$ and belongs to a finite-codimension linear subspace.