[Sur l'équation cohomologique pour les échanges d'intervalles]
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.
On présente une classe explicite d'échanges d'intervalles T, de mesure pleine, pour laquelle l'équation cohomologique Ψ−Ψ∘T=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.
Accepté le :
Publié le :
Stefano Marmi 1, 2 ; Pierre Moussa 3 ; Jean-Christophe Yoccoz 4
@article{CRMATH_2003__336_11_941_0,
author = {Stefano Marmi and Pierre Moussa and Jean-Christophe Yoccoz},
title = {On the cohomological equation for interval exchange maps},
journal = {Comptes Rendus. Math\'ematique},
pages = {941--948},
publisher = {Elsevier},
volume = {336},
number = {11},
year = {2003},
doi = {10.1016/S1631-073X(03)00222-X},
language = {en},
}
TY - JOUR AU - Stefano Marmi AU - Pierre Moussa AU - Jean-Christophe Yoccoz TI - On the cohomological equation for interval exchange maps JO - Comptes Rendus. Mathématique PY - 2003 SP - 941 EP - 948 VL - 336 IS - 11 PB - Elsevier DO - 10.1016/S1631-073X(03)00222-X LA - en ID - CRMATH_2003__336_11_941_0 ER -
Stefano Marmi; Pierre Moussa; Jean-Christophe Yoccoz. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00222-X/
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