Weakly dissipative systems in celestial mechanics

We investigate the dynamics associated to nearly integrable dissipative systems, with particular reference to some models of Celestial Mechanics which can be described in a weakly dissipative framework. We start by studying some paradigmatic models provided by the dissipative standard maps in two- and four-dimensions. The dynamical investigation is performed applying frequency analysis and computing the differential fast Lyapunov indicators. After recalling a few properties of adiabatic invariants, we provide some examples of nearly integrable dissipative systems borrowed from Celestial Mechanics, and precisely the spin-orbit coupling and the three-body problem. We conclude with a discussion on the existence of periodic orbits in dissipative autonomous and non-autonomous systems. © 2007 Springer-Verlag Berlin Heidelberg