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July  2005, 12(4): 569-594. doi: 10.3934/dcds.2005.12.569

Exponential stability for the resonant D'Alembert model of celestial mechanics

Luca Biasco 1, and  Luigi Chierchia 1,

1. 

Dipartimento di Matematica, Università "Roma Tre", Largo S. L. Murialdo 1, 00146 Roma, Italy

Received  May 2004 Revised  May 2004 Published  January 2005

We consider the classical D'Alembert Hamiltonian model for a rotationally symmetric planet revolving on Keplerian ellipse around a fixed star in an almost exact "day/year" resonance and prove that, notwithstanding proper degeneracies, the system is stable for exponentially long times, provided the oblateness and the eccentricity are suitably small.
Keywords: Hamiltonian systems, action-angle variables, proper degeneracies, nonlinear dynamics, celestial mechanics, KAM and Nekhoroshev theory, D'Alembert model, stability, fast averaging.
Mathematics Subject Classification: 37C75, 70H08, 70K43, 70K45, 34D10, 34C2.
Citation: Luca Biasco, Luigi Chierchia. Exponential stability for the resonant D'Alembert model of celestial mechanics. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 569-594. doi: 10.3934/dcds.2005.12.569
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