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Studies of dynamical stability (chaotic versus regular motion) in galacticdynamics often rely on static analytical models of the total gravitationalpotential. Potentials based upon self-consistent N-body simulations offer morerealistic models, fully incorporating the time-dependent nature of the systems.Here we aim at analysing the fractions of chaotic motion within differentmorphological components of the galaxy. We wish to investigate how the presenceof chaotic orbits evolves with time, and how their spatial distribution isassociated with morphological features of the galaxy. We employ atime-dependent analytical potential model that was derived from an N-bodysimulation of a strongly barred galaxy. With this analytical potential we mayfollow the dynamical evolution of ensembles of orbits. Using the GeneralizedAlignment Index (GALI) chaos detection method, we study the fraction of chaoticorbits, sampling the dynamics of both the stellar disc and of the dark matterhalo. Within the stellar disc, the global trend is for chaotic motion todecrease in time, specially in the region of the bar. We scrutinized thedifferent changes of regime during the evolution (orbits that are permanentlychaotic, permanently regular, those that begin regular and end chaotic, andthose that begin chaotic and end regular), tracing the types of orbits back totheir common origins. Within the dark matter halo, chaotic motion alsodecreases globally in time. The inner halo (r < 5 kpc) is where most chaoticorbits are found and it is the only region where chaotic orbits outnumberregular orbits, in the early evolution.

Chaotic motion and the evolution of morphological components in a time-dependent model of a barred galaxy within a dark matter halo