Orbital dynamics in galactic potentials under mass transfer

Context. Time-dependent potentials are common in galactic systems that undergo significant evolution, interactions, or encounters with other galaxies, or when there are dynamic processes such as star formation and merging events. Recent studies show that an ensemble approach along with the so-called snapshot framework in the theory of dynamical systems provide a powerful tool to analyze the time-dependent dynamics. Aims. In this work, we aim to explore and quantify the phase space structure and dynamical complexity in time-dependent galactic potentials consisting of multiple components. Methods. We applied the classical method of Poincaré surface of sections to analyze the phase space structure in a chaotic Hamiltonian system subjected to parameter drift. This, however, makes sense only when the evolution of a large ensemble of initial conditions is followed. Numerical simulations explore the phase space structure of such ensembles while the system undergoes a continuous parameter change. The pair-wise average distance of ensemble members allowed us to define a generalized Lyapunov exponent, which might also be time-dependent, to describe the system stability. Results. We provide a comprehensive dynamical analysis of the system under circumstances where linear mass transfer occurs between the disk and bulge components of the model.