For one dimensional dynamical systems it is well know from the work of Yoccoz that the optimal arithmetic condition to bypass the small divisor problem in the analytic class in the local setting (for example to analytically linearize circle analytic diffeomorphisms that are close to a rotation) is the so called Bryuno condition. In a joint work with Livia Corsi we provide an arithmetic condition that is weaker then the Bryuno condition for which it is still possible to bypass the small divisor problem in higher dimension. The scheme will be provided for analytic diffeomorphisms of the Torus that are close to a rotation and for which the rotation vector exists.
org: PROCESI Michela