These lectures are devoted to the main results of classical perturbation theory. We start by recalling the methods of Hamiltonian dynamics., the problem of small divisors, the series of Lindstedt and the method of normal form. Then we discuss the theorem of Kolmogorov with an application to the Sun-Jupiter-Saturn problem in Celestial Mechanics. Finally we discuss the problem of long-time stability, by discussing the concept of exponential stability as introduced by Moser and Littlewood and fully exploited by Nekhoroshev. The phenomenon of superexponential stability is also recalled.

Canonical perturbation theory for nearly integrable systems / A. Giorgilli, U. Locatelli - In: Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems / [a cura di] B.A. Steves, A.J. Maciejewski, M. Hendry. - [s.l] : Springer, 2006. - ISBN 9781402047046. - pp. 1-41 (( Intervento presentato al 11. convegno Chaotic Worlds: From Order to Disorder in Gravitational N-Body Dynamical Systems tenutosi a Cortina d Ampezzo nel 2003 [10.1007/978-1-4020-4706-0_1].

Canonical perturbation theory for nearly integrable systems

A. Giorgilli
Primo
;
U. Locatelli
Ultimo
2006

Abstract

These lectures are devoted to the main results of classical perturbation theory. We start by recalling the methods of Hamiltonian dynamics., the problem of small divisors, the series of Lindstedt and the method of normal form. Then we discuss the theorem of Kolmogorov with an application to the Sun-Jupiter-Saturn problem in Celestial Mechanics. Finally we discuss the problem of long-time stability, by discussing the concept of exponential stability as introduced by Moser and Littlewood and fully exploited by Nekhoroshev. The phenomenon of superexponential stability is also recalled.
Hamiltonian systems; perturbation theory; normal forms; KAM theory; Nekhoroshev's theorem; planetary systems
Settore MAT/07 - Fisica Matematica
Settore FIS/05 - Astronomia e Astrofisica
NATO Advanced Study Institute
Book Part (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/243986
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