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2018 A normal form à la Moser for diffeomorphisms and a generalization of Rüssmann's translated curve theorem to higher dimensions
Jessica Elisa Massetti
Anal. PDE 11(1): 149-170 (2018). 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.

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Jessica Elisa Massetti. "A normal form à la Moser for diffeomorphisms and a generalization of Rüssmann's translated curve theorem to higher dimensions." Anal. PDE 11 (1) 149 - 170, 2018. https://doi.org/10.2140/apde.2018.11.149

Information

Received: 31 August 2016; Revised: 14 June 2017; Accepted: 28 July 2017; Published: 2018
First available in Project Euclid: 20 December 2017

zbMATH: 06789262
MathSciNet: MR3707294
Digital Object Identifier: 10.2140/apde.2018.11.149

Subjects:
Primary: 37C05, 37J40, 37-XX

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.11 • No. 1 • 2018
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