Revealing the escape mechanism of three-dimensional orbits in a tidally
  limited star cluster
  The aim of this work is to explore the escape process of three-dimensional
orbits in a star cluster rotating around its parent galaxy in a circular orbit.
The gravitational field of the cluster is represented by a smooth, spherically
symmetric Plummer potential, while the tidal approximation was used to model
the steady tidal field of the galaxy. We conduct a thorough numerical analysis
distinguishing between regular and chaotic orbits as well as between trapped
and escaping orbits, considering only unbounded motion for several energy
levels. It is of particular interest to locate the escape basins towards the
two exit channels and relate them with the corresponding escape times of the
orbits. For this purpose, we split our investigation into three cases depending
on the initial value of the $z$ coordinate which was used for launching the
stars. The most noticeable finding is that the majority of stars initiated very
close to the primary $(x,y)$ plane move in chaotic orbits and they remain
trapped for vast time intervals, while orbits with relatively high values of
$z_0$ on the other hand, form well-defined basins of escape. It was also
observed, that for energy levels close to the critical escape energy the escape
rates of orbits are large, while for much higher values of energy most of the
orbits have low escape periods or they escape immediately to infinity. We hope
our outcomes to be useful for a further understanding of the dissolution
process and the escape mechanism in open star clusters.
