  Accretion onto black holes and compact stars brings material in a zone of
strong gravitational and electromagnetic fields. We study dynamical properties
of motion of electrically charged particles forming a highly diluted medium (a
corona) in the regime of strong gravity and large-scale (ordered) magnetic
field. We start our work from a system that allows regular motion, then we
focus on the onset of chaos. To this end, we investigate the case of a rotating
black hole immersed in a weak, asymptotically uniform magnetic field. We also
consider a magnetic star, approximated by the Schwarzschild metric and a test
magnetic field of a rotating dipole. These are two model examples of systems
permitting energetically bound, off-equatorial motion of matter confined to the
halo lobes that encircle the central body. Our approach allows us to address
the question of whether the spin parameter of the black hole plays any major
role in determining the degree of the chaoticness. To characterize the motion,
we construct the Recurrence Plots (RP) and we compare them with Poincar\'e
surfaces of section. We describe the Recurrence Plots in terms of the
Recurrence Quantification Analysis (RQA), which allows us to identify the
transition between different dynamical regimes. We demonstrate that this new
technique is able to detect the chaos onset very efficiently, and to provide
its quantitative measure. The chaos typically occurs when the conserved energy
is raised to a sufficiently high level that allows the particles to traverse
the equatorial plane. We find that the role of the black-hole spin in setting
the chaos is more complicated than initially thought.
