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Article Dans Une Revue Advances in Mathematics Année : 2020

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

Résumé

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.
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Dates et versions

hal-01188980 , version 1 (01-09-2015)
hal-01188980 , version 2 (20-03-2019)

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Abed Bounemoura, Bassam Fayad, Laurent Niederman. Super-exponential stability for generic real-analytic elliptic equilibrium points. Advances in Mathematics, 2020, 366, ⟨10.1016/j.aim.2020.107088⟩. ⟨hal-01188980v2⟩
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