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arXiv · 1608.03500

Normal form à la Moser for diffeomorphisms and generalization of Rüssmann's translated curve theorem to higher dimension

Jessica Elisa Massetti
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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.

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Jessica Elisa Massetti. 2016-08-11. Normal form à la Moser for diffeomorphisms and generalization of Rüssmann's translated curve theorem to higher dimension. https://doi.org/10.2140/apde.2018.11.149

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