Double exponential stability for generic real-analytic elliptic equilibrium points
Bounemoura, Abed; Fayad, Bassam; Niederman, Laurent (2015), Double exponential stability for generic real-analytic elliptic equilibrium points. https://basepub.dauphine.fr/handle/123456789/17158
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-01188980
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
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Abstract (EN)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. We actually prove a more general statement assuming the frequency is only non-resonant. This improves previous results where much stronger non-generic assumptions were required.
Subjects / Keywordselliptic equilibrium points
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