Nearly-integrable dissipative systems and celestial mechanics

Abstract

The influence of dissipative effects on classical dynamical models of Celestial Mechanics is of basic importance. We introduce the reader to the subject, giving classical examples found in the literature, like the standard map, the Hénon map, the logistic mapping. In the framework of the dissipative standard map, we investigate the existence of periodic orbits as a function of the parameters. We also provide some techniques to compute the breakdown threshold of quasi-periodic attractors. Next, we review a simple model of Celestial Mechanics, known as the spin-orbit problem which is closely linked to the dissipative standard map. In this context we present the conservative and dissipative KAM theorems to prove the existence of quasi-periodic tori and invariant attractors. We conclude by reviewing some dissipative models of Celestial Mechanics. Among the rotational dynamics we consider the Yarkovsky and YORP effects; within the three-body problem we introduce the so-called Stokes and Poynting-Robertson effects.