Some KAM applications to Celestial Mechanics

Alessandra Celletti

doi:10.3934/dcdss.2010.3.533

Article Contents

2010, Volume 3, Issue 4: 533-544. Doi: 10.3934/dcdss.2010.3.533

This issue Previous Article A geometric fractional monodromy theorem Next Article Properly-degenerate KAM theory (following V. I. Arnold)

Some KAM applications to Celestial Mechanics

Alessandra Celletti^1,

1.
Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma

Received: March 31, 2009

Revised: April 30, 2010

Published: November 2010

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Abstract

The existence of invariant tori in Celestial Mechanics has been widely investigated through implementations of the Kolmogorov-Arnold-Moser (KAM) theory. We provide an introduction to some results on the existence of maximal and low-dimensional, rotational and librational tori for models of Celestial Mechanics: from the spin--orbit problem to the three-body and planetary models. We also briefly review a result on dissipative invariant attractors for the spin-orbit problem, whose existence is proven through a dissipative KAM theorem.

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Mathematics Subject Classification: Primary: 70E50, 37N05, 70F15.

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