Two–layer model via non–quasi–periodic normal form theory

The “two–layer model” is a 2+12 degrees–of–freedom non–autonomous dynamical system consisting of a massive, ellipsoidal (possibly spheric) body made of two layers – a hard core and a viscous fluid – revolving about a major planet or a star. We assume that the rotation and the two revolution periods (of core and shell) are close to a resonance, and aim to investigate, in a rigorous way, the mathematical conditions which maintain the resonant motion. In a previous article (Pinzari et al. in Celest Mech Dyn Astron 136(5):39, 2024), we discussed the phenomenon known as “capture into resonance”, via qualitative arguments supported by numerical findings. In this paper, we reframe the model along the lines of a suitable version of (which we refer to as “non–quasi–periodic”) normal form theory and provide an explicit amount of the resonance trapping time, which is estimated as exponentially–long, in terms of the small parameters of the system.