Cohomological equations for suspension flows over Vershik automorphisms

The cohomological equation for Roth type interval exchange maps

We exhibit an explicit full measure class of minimal interval exchange maps T for which the cohomological equation $Ψ-Ψ\circ T=Φ$ has a bounded solution $Ψ$ provided that the datum $Φ$ belongs to a finite codimension subspace of the space of functions having on each interval a derivative of bounded variation. The class of interval exchange maps is characterized in terms of a diophantine condition of ``Roth type'' imposed to an acceleration of the Rauzy--Veech--Zorich continued fraction expansion associated to T. CONTENTS 0. Introduction 1. The continued fraction algorithm for interval exchange…