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Normal forms for perturbations of systems possessing a Diophantine invariant torus

Published online by Cambridge University Press:  12 December 2017

JESSICA ELISA MASSETTI
JESSICA ELISA MASSETTI*
Affiliation:
Università degli Studi Roma Tre, Dipartimento di Matematica e Fisica, Largo San L. Murialdo 1, 00146 Roma, Italy email jmassetti@mat.uniroma3.it
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Abstract

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We give a new proof of Moser’s 1967 normal-form theorem for real analytic perturbations of vector fields possessing a reducible Diophantine invariant quasi-periodic torus. The proposed approach, based on an inverse function theorem in analytic class, is flexible and can be adapted to several contexts. This allows us to prove in a unified framework the persistence, up to finitely many parameters, of Diophantine quasi-periodic normally hyperbolic reducible invariant tori for vector fields originating from dissipative generalizations of Hamiltonian mechanics. As a byproduct, generalizations of Herman’s twist theorem and Rüssmann’s translated curve theorem are proved.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 8 , August 2019 , pp. 2176 - 2222
Copyright
© Cambridge University Press, 2017 

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