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Étant donnée une fonction régulière de moyenne nulle sur le tore de dimension , il est facile de voir que ses intégrales ergodiques au-dessus d’un flot de translation “générique”sont bornées. Il y a une dizaine d’années, A. Zorich a observé numériquement une croissance en puissance du temps de ces intégrales ergodiques au-dessus de flots d’hamiltoniens (non-exacts) “génériques”sur des surfaces de genre supérieur ou égal à , et Kontsevich et Zorich ont proposé une explication (conjecturelle) de...
We present a proof of Herman’s Last Geometric Theorem asserting that if is a smooth diffeomorphism of the annulus having the intersection property, then any given -invariant smooth curve on which the rotation number of is Diophantine is accumulated by a positive measure set of smooth invariant curves on which is smoothly conjugated to rotation maps. This implies in particular that a Diophantine elliptic fixed point of an area preserving diffeomorphism of the plane is stable. The remarkable...
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