Publikace ÚTF

We continue the study of time-like geodesic dynamics in exact static, axially and reflection
symmetric space–times describing the fields of a Schwarzschild black hole surrounded by thin
discs or rings. In the previous paper, the rise (and decline) of geodesic chaos with ring/disc mass
and position and with test particle energy was revealed on Poincar´e sections, on time series of
position or velocity and their power spectra, and on time evolution of the orbital ‘latitudinal
action’. In agreement with the KAM theory of nearly integrable dynamical systems and with
the results observed in similar gravitational systems in the literature, we found orbits of
very different degrees of chaoticity in the phase space of perturbed fields. Here we compare
selected orbits in more detail and try to classify them according to the characteristics of the
corresponding phase-variable time series, mainly according to the shape of the time-series
power spectra, and also applying two recurrence methods: the method of ‘average directional
vectors’, which traces the directions in which the trajectory (recurrently) passes through a
chosen phase-space cell, and the ‘recurrence-matrix’ method, which consists of statistics over
the recurrences themselves. All the methods proved simple and powerful, while it is interesting
to observe how they differ in sensitivity to certain types of behaviour.