On the cohomological equation for interval exchange maps

Abstract

We exhibit an explicit full measure class of minimal interval exchange maps T for which the cohomological equation Ψ− Ψ∘ 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. To cite this article: S. Marmi et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).