Super-exponential stability for generic real-analytic elliptic equilibrium points

We consider the dynamics in a neighborhood of an elliptic equilibrium point with a Diophantine frequency of a symplectic real analytic vector field and we prove the following result of effective stability. Generically, both in a topological and measure-theoretical sense, any solution starting suffic...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2020-06, Vol.366, p.107088, Article 107088
Main Authors: Bounemoura, Abed, Fayad, Bassam, Niederman, Laurent
Format: Article
Language:English
Subjects:
Dynamical Systems
Equilibrium points
Hamiltonian systems
Mathematics
Stability theory
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Summary:We consider the dynamics in a neighborhood of an elliptic equilibrium point with a Diophantine frequency of a symplectic real analytic vector field and we prove the following result of effective stability. Generically, both in a topological and measure-theoretical sense, any solution starting sufficiently close to the equilibrium point remains close to it for an interval of time which is doubly exponentially large with respect to the inverse of the distance to the equilibrium point.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2020.107088