FM 01-8; mp_arc 00-??? nlin/CD 0007???
Author: V. Mastropietro
Title: Arnold diffusion and the D'Alembert precession problem
Abstract: A planet can be described by an homogeneous rigid ellipsoid with flatness $\h$, moving on a Keplerian orbit around a star and subject only to Newtonian forces. It was proposed in 1994 in [CG] that, for suitable initial data, the precession cone can change $O(1)$ in a finite time, no matter how small $\h$ is, as a consequence of Arnold diffusion mechanism. One can start introducing some simplifications in the original model, neglecting a term in its Hamiltonian so that the problem is reduced to a priori unstable three time scale system; for such systems a general theory of Arnold diffusion can indeed be developed (mainly in [CG],[G3],[GGM1],[GGM2]). In this paper we will review the main results about Arnold diffusion in three time scale a priori unstable systems and we discuss their relevance for a complete understanding of the precession problem.
Key words: Arnold diffusion, D'Alembert problem.
Vieri Mastropietro
Universita' di Roma 2, Dip. Matematica
Via Fontanile di Carcaricola
00133 Roma, Italia