Marco Sansottera
via Saldini 50, 20133, Milano, Italy
Dipartimento di Matematica, Università degli Studi di Milano
Publications:
Bambusi D., Fusè A., Sansottera M.
Exponential Stability in the Perturbed Central Force Problem
2018, vol. 23, no. 78, pp. 821841
Abstract
We consider the spatial central force problem with a real analytic potential. We prove that for all analytic potentials, but for the Keplerian and the harmonic ones, the Hamiltonian fulfills a nondegeneracy property needed for the applicability of Nekhoroshevâ€™s
theorem. We deduce stability of the actions over exponentially long times when the system is subject to an arbitrary analytic perturbation. The case where the central system is put in interaction with a slow system is also studied and stability over exponentially long time is proved.

Giorgilli A., Locatelli U., Sansottera M.
Secular Dynamics of a Planar Model of the SunJupiterSaturnUranus System; Effective Stability in the Light of Kolmogorov and Nekhoroshev Theories
2017, vol. 22, no. 1, pp. 5477
Abstract
We investigate the longtime stability of the SunJupiterSaturnUranus system by considering a planar secular model, which can be regarded as a major refinement of the approach first introduced by Lagrange. Indeed, concerning the planetary orbital revolutions, we improve the classical circular approximation by replacing it with a solution that is invariant up to order two in the masses; therefore, we investigate the stability of the secular system for rather small values of the eccentricities. First, we explicitly construct a Kolmogorov normal form to find an invariant KAM torus which approximates very well the secular orbits. Finally, we adapt the approach that underlies the analytic part of Nekhoroshevâ€™s theorem to show that there is a neighborhood of that torus for which the estimated stability time is larger than the lifetime of the Solar System. The size of such a neighborhood, compared with the uncertainties of the astronomical observations, is about ten times smaller.
