Kovács Tamás (Eötvös Loránd University)

The dynamics of an oblate satellite in a fixed elliptical orbit, with its spin axis perpendicular to the orbital plane around a spherical planet, exhibit rich coupling between rotation and orbital motion, known as spin-orbit resonance. It is well known that the phase space of low-dimensional deterministic Hamiltonian systems contains regions of both chaotic and regular motion—namely, chaotic bands and invariant curves (KAM tori)—depending on the initial conditions and system parameters. In the steady-state case, these structures remain stationary. However, when system parameters change over time, due to various internal or external influences, the geometry of phase space evolves accordingly. This necessitates a shift from traditional single-trajectory analysis to an ensemble-based approach, enabling a consistent framework to describe phase space structures in non-autonomous Hamiltonian systems. In this context, we also generalize the classical Lyapunov exponent to account for explicit time dependence, providing a numerical stability measure for the evolving dynamics. Finally, we propose a preliminary analytical description of the time-dependent phase space structures and their evolution.