Perturbative methods and synchronous resonances in Celestial Mechanics

Abstract

We study the stability of some model problems in Celestial Mechanics, focusing on the dynamics around synchronous resonances, namely 1:1 commensurabilities among the main characteristic frequencies. In particular, we illustrate the following examples: the Earth's satellites dynamics, orbital asteroids, the rotational dynamics. Within such model problems we analyze, respectively, the stability of the Zeipel-Lidov-Kozai integral, the triangular Lagrangian points, the spin orbit resonance. Stability results are obtained through perturbative methods, precisely implementation of normal forms, Nekhoroshev-type estimates or KAM theory.