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

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

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.
Citation: Luca Biasco, Luigi Chierchia. Exponential stability for the resonant D'Alembert model of celestial mechanics. Discrete & Continuous Dynamical Systems - A, 2005, 12 (4) : 569-594. doi: 10.3934/dcds.2005.12.569
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