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Analytic Lagrangian tori for the planetary many-body problem

Published online by Cambridge University Press:  01 June 2009

LUIGI CHIERCHIA  and
FABIO PUSATERI
LUIGI CHIERCHIA
Affiliation:
Dipartimento di Matematica, Università ‘Roma Tre’, Largo S. L. Murialdo 1, I-00146 Roma, Italy (email: [email protected])
FABIO PUSATERI
Affiliation:
Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012, USA (email: [email protected])
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Abstract

In 2004, Féjoz [Démonstration du ‘théoréme d’Arnold’ sur la stabilité du système planétaire (d’après M. Herman). Ergod. Th. & Dynam. Sys.24(5) (2004), 1521–1582], completing investigations of Herman’s [Démonstration d’un théoréme de V.I. Arnold. Séminaire de Systémes Dynamiques et manuscripts, 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. Uspekhi Mat. Nauk. 18(6(114)) (1963), 91–192] on the planetary many-body problem, establishing, in particular, the existence of a positive measure set of smooth (C∞) 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. Dynamics2(6) (2001), 119–203], we prove the above result in the real-analytic class.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 3 , June 2009 , pp. 849 - 873
Copyright
Copyright © Cambridge University Press 2009

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