2003/04/28 by Marmi, Stefano, Moussa, Pierre, Yoccoz, Jean-Christophe
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.math/0304469
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. Contents 0. French abridged version 1. Interval exchange maps and the cohomological equation. Main Theorem 2. Rauzy--Veech--Zorich continued fraction algorithm and its acceleration 3. Special Birkhoff sums 4. The Diophantine condition 5. Sketch of the proof of the theorem