`a`
Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

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

Pages: 569 - 594, Volume 12, Issue 4, April 2005      doi:10.3934/dcds.2005.12.569

 
       Abstract        Full Text (418.1K)       Related Articles

Luca Biasco - Dipartimento di Matematica, Università "Roma Tre", Largo S. L. Murialdo 1, 00146 Roma, Italy (email)
Luigi Chierchia - Dipartimento di Matematica, Università "Roma Tre", Largo S. L. Murialdo 1, 00146 Roma, Italy (email)

Abstract: 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:  KAM and Nekhoroshev theory, stability, nonlinear dynamics, Hamiltonian systems,D'Alembert model, celestial mechanics, proper degeneracies, fast averaging, action-angle variables
Mathematics Subject Classification:  37C75, 70H08, 70K43, 70K45, 34D10, 34C29.

Received: May 2004;      Revised: May 2004;      Available Online: January 2005.