A novel approach derives KAM-type linearization theorems directly from the stable foliation of a renormalization operator, illustrated with a version of Arnold's theorem and persistence of Herman rings in two-dimensional maps.
Risler, Lin\' e arisation des perturbations holomorphes des rotations et applications , M\' e m
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Rotation domains for maps of bounded type
A novel approach derives KAM-type linearization theorems directly from the stable foliation of a renormalization operator, illustrated with a version of Arnold's theorem and persistence of Herman rings in two-dimensional maps.