Double exponential stability of quasi-periodic motion in Hamiltonian systems

We prove that generically, both in a topological and measure-theoretical sense, an invariant Lagrangian Diophantine torus of a Hamiltonian system is doubly exponentially stable in the sense that nearby solutions remain close to the torus for an interval of time which is doubly exponentially large wi...

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Bibliographic Details
Published in:Communications in mathematical physics 2017, Vol.350 (1)
Main Authors: Bounemoura, Abed, Fayad, Bassam, Niederman, Laurent
Format: Article
Language:English
Subjects:
Dynamical Systems
Mathematics
Online Access:Get full text
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Summary:We prove that generically, both in a topological and measure-theoretical sense, an invariant Lagrangian Diophantine torus of a Hamiltonian system is doubly exponentially stable in the sense that nearby solutions remain close to the torus for an interval of time which is doubly exponentially large with respect to the inverse of the distance to the torus. We also prove that for an arbitrary small perturbation of a generic integrable Hamiltonian system, there is a set of almost full positive Lebesgue measure of KAM tori which are doubly exponentially stable. Our results hold true for real-analytic but more generally for Gevrey smooth systems.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-016-2782-9