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.

Massetti, J.E. (2019). Normal forms for perturbations of systems possessing a Diophantine invariant torus. ERGODIC THEORY & DYNAMICAL SYSTEMS, 39(8), 2176-2222 [10.1017/etds.2017.116].

Normal forms for perturbations of systems possessing a Diophantine invariant torus

Massetti J. E.
2019-01-01

Abstract

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.
2019
Massetti, J.E. (2019). Normal forms for perturbations of systems possessing a Diophantine invariant torus. ERGODIC THEORY & DYNAMICAL SYSTEMS, 39(8), 2176-2222 [10.1017/etds.2017.116].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/359609
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