We prove a discrete time analogue of Moser's normal form (1967) 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 codimension. Under convenient nondegeneracy assumptions on the diffeomorphisms under study (a torsion property for example), this codimension 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.

Massetti, J.E. (2018). A normal form à la moser for diffeomorphisms and a generalization of Rüssmann'S translated curve theorem to higher dimensions. ANALYSIS & PDE, 11(1), 149-170 [10.2140/apde.2018.11.149].

A normal form à la moser for diffeomorphisms and a generalization of Rüssmann'S translated curve theorem to higher dimensions

Massetti J. E.
2018-01-01

Abstract

We prove a discrete time analogue of Moser's normal form (1967) 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 codimension. Under convenient nondegeneracy assumptions on the diffeomorphisms under study (a torsion property for example), this codimension 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.
2018
Massetti, J.E. (2018). A normal form à la moser for diffeomorphisms and a generalization of Rüssmann'S translated curve theorem to higher dimensions. ANALYSIS & PDE, 11(1), 149-170 [10.2140/apde.2018.11.149].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/359611
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