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Nekhoroshev estimates for steep real-analytic elliptic equilibrium points

Bounemoura, Abed; Fayad, Bassam; Niederman, Laurent (2019), Nekhoroshev estimates for steep real-analytic elliptic equilibrium points, Nonlinearity, 33, 1. 10.1088/1361-6544/ab4c89

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
Nonlinearity
Volume
33
Number
1
Publisher
IOP Science
Publication identifier
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Author(s)
Bounemoura, Abed
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Fayad, Bassam
Institut de Mathématiques de Jussieu - Paris Rive Gauche [IMJ-PRG]
Niederman, Laurent
Institut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]
Abstract (EN)
We prove that steep real-analytic elliptic equilibrium points are exponentially stable, generalizing results which were known only under a convexity assumption. This proves the general case of a conjecture of Nekhoroshev. This result is also an important step in our proof that generically, both in a topological and measure-theoretical sense, equilibrium points are super-exponentially stable.
Subjects / Keywords
real-analytic elliptic equilibrium points; Nekhoroshev