Quasi-periodic attractors and spin-orbit resonances

Introduction: ``Mechanical systems, in real life, are typically dissipative, and perfectly conservative systems arise as mathematical abstractions. In this paper, we shall consider nearly-conservative mechanical systems having in mind applications to celestial mechanics. In particular we are interested in the spin-orbit model for an oblate planet (satellite) whose center of mass revolves around a `fixed' star; the planet is not completely rigid and averaged effects of tides, which bring in dissipation, are taken into account. We shall see that a mathematical theory of such systems is consistent with the strange case of Mercury, which is the only planet or satellite in the solar system being stacked in a 3:2 spin/orbit resonance (i.e., it turns three times around its rotational spin axis, while it makes one revolution around the Sun).''