Dynamical Systems
On the cohomological equation for interval exchange maps
Comptes Rendus. Mathématique, Volume 336 (2003) no. 11, pp. 941-948.

We exhibit an explicit full measure class of minimal interval exchange maps T for which the cohomological equation ΨΨT=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.

On présente une classe explicite d'échanges d'intervalles T, de mesure pleine, pour laquelle l'équation cohomologique ΨΨT=Φ admet une solution bornée Ψ, à condition que la donnée Φ appartienne à un sous-espace de codimension finie de l'espace des fonctions dont la dérivée sur chaque intervalle est de variation bornée.

Cette classe est définie par une condition diophantienne « de type Roth » exprimé dans une variante du développement en fraction continue de Rauzy–Veech–Zorich associé à T.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(03)00222-X
Marmi, Stefano 1, 2; Moussa, Pierre 3; Yoccoz, Jean-Christophe 4

1 Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 206, Loc. Rizzi, 33100 Udine, Italy
2 Scuola Normale Superiore, Piazza dei Cavalieri 7, Pisa, Italy
3 Service de physique théorique, CEA/Saclay, 91191 Gif-Sur-Yvette, France
4 Collège de France, 3, rue d'Ulm, 75005 Paris, France
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Marmi, Stefano; Moussa, Pierre; Yoccoz, Jean-Christophe. On the cohomological equation for interval exchange maps. Comptes Rendus. Mathématique, Volume 336 (2003) no. 11, pp. 941-948. doi : 10.1016/S1631-073X(03)00222-X. http://www.numdam.org/articles/10.1016/S1631-073X(03)00222-X/

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