In 2004 J. Féjoz [Démonstration du ‘théorème d’Arnold’ sur la stabilité du système planétaire (d’après M. Herman). Ergod. Th. & Dynam. Sys, 24(5):1521-1582, 2004], completing investigations of M. Herman’s [Démonstration d’un théorème de V.I. Arnold. Séminaire de Systèmes Dynamiques et manuscripts, Université D. Diderot, Paris 7, 1998], gave a complete proof of “Arnold’s Theorem” [V.I. Arnol’d. Small Denominators and Problems of Stability of Motion in Classical and Celestial Mechanics. Usephi Mat. Nauk, 18(6 (114)):91-192, 1963] on the planetary many–body problem, establishing, in particular, the existence of a positive measure set of smooth (C1) Lagrangian invariant tori for the planetary many–body problem. Here, using Rüßmann’s 2001 KAM theory [H. Rüßmann. Invariant Tori in Non-Degenerate Nearly Integrable Hamiltonian Systems. R. & C. Dynamics, 2(6):119-203, 2001], we prove the above result in the real–analytic class.

Chierchia, L., Pusateri, F. (2009). Analytic Lagrangian tori for the planetary manybody problem. ERGODIC THEORY & DYNAMICAL SYSTEMS, 29, 849-873 [10.1017/S0143385708000503].

Analytic Lagrangian tori for the planetary manybody problem

CHIERCHIA, Luigi;
2009-01-01

Abstract

In 2004 J. Féjoz [Démonstration du ‘théorème d’Arnold’ sur la stabilité du système planétaire (d’après M. Herman). Ergod. Th. & Dynam. Sys, 24(5):1521-1582, 2004], completing investigations of M. Herman’s [Démonstration d’un théorème de V.I. Arnold. Séminaire de Systèmes Dynamiques et manuscripts, Université D. Diderot, Paris 7, 1998], gave a complete proof of “Arnold’s Theorem” [V.I. Arnol’d. Small Denominators and Problems of Stability of Motion in Classical and Celestial Mechanics. Usephi Mat. Nauk, 18(6 (114)):91-192, 1963] on the planetary many–body problem, establishing, in particular, the existence of a positive measure set of smooth (C1) Lagrangian invariant tori for the planetary many–body problem. Here, using Rüßmann’s 2001 KAM theory [H. Rüßmann. Invariant Tori in Non-Degenerate Nearly Integrable Hamiltonian Systems. R. & C. Dynamics, 2(6):119-203, 2001], we prove the above result in the real–analytic class.
Chierchia, L., Pusateri, F. (2009). Analytic Lagrangian tori for the planetary manybody problem. ERGODIC THEORY & DYNAMICAL SYSTEMS, 29, 849-873 [10.1017/S0143385708000503].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/159187
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