Normal form à la Moser for diffeomorphisms and generalization of Rüssmann's translated curve theorem to higher dimension
arXiv:1608.03500 · doi:10.2140/apde.2018.11.149
Abstract
We prove a discrete time analogue of 1967 Moser's normal form of real analytic perturbations of vector fields possessing an invariant, reducible, Diophantine torus; in the case of diffeomorphisms too, the persistence of such an invariant torus is a phenomenon of finite co-dimension. Under convenient non-degeneracy assumptions on the diffeomorphisms under study (torsion property for example), this co-dimension can be reduced. As a by-product we obtain generalizations of Rüssmann's translated curve theorem in any dimension, by a technique of elimination of parameters.
arXiv admin note: text overlap with arXiv:1512.01486, arXiv:1511.02733