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 Russmann'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 Russmann's translated curve theorem in any dimension, by a technique of elimination of parameters.File | Dimensione | Formato | |
---|---|---|---|
discrete_moser-2.pdf
solo utenti autorizzati
Tipologia:
Documento in Pre-print
Licenza:
Copyright dell'editore
Dimensione
366.79 kB
Formato
Adobe PDF
|
366.79 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.