A normal form à la Moser for diffeomorphisms and a generalization of Rüssmann’s translated curve theorem to higher dimensions

Massetti, Jessica Elisa

doi:10.2140/apde.2018.11.149

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

Jessica Elisa Massetti

Vol. 11 (2018), No. 1, 149–170

DOI: 10.2140/apde.2018.11.149

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.

Keywords

normal forms, Diophantine tori, KAM, counter terms, translated tori

Mathematical Subject Classification 2010

Primary: 37-XX, 37C05, 37J40

Milestones

Received: 31 August 2016

Revised: 14 June 2017

Accepted: 28 July 2017

Published: 17 September 2017

Authors

Jessica Elisa Massetti
Università degli Studi Roma Tre Dipartimento di Matematica e Fisica Sezione Matematica Rome Italy

Vol. 11, No. 1, 2018