Unraveling the escape dynamics and the nature of the normally hyperbolic
  invariant manifolds in tidally limited star clusters
  The escape mechanism of orbits in a star cluster rotating around its parent
galaxy in a circular orbit is investigated. A three degrees of freedom model is
used for describing the dynamical properties of the Hamiltonian system. The
gravitational field of the star cluster is represented by a smooth and
spherically symmetric Plummer potential. We distinguish between ordered and
chaotic orbits as well as between trapped and escaping orbits, considering only
unbounded motion for several energy levels. The Smaller Alignment Index (SALI)
method is used for determining the regular or chaotic nature of the orbits. The
basins of escape are located and they are also correlated with the
corresponding escape time of the orbits. Areas of bounded regular or chaotic
motion and basins of escape were found to coexist in the $(x,z)$ plane. The
properties of the normally hyperbolic invariant manifolds (NHIMs), located in
the vicinity of the index-1 Lagrange points $L_1$ and $L_2$, are also explored.
These manifolds are of paramount importance as they control the flow of stars
over the saddle points, while they also trigger the formation of tidal tails
observed in star clusters. Bifurcation diagrams of the Lyapunov periodic orbits
as well as restrictions of the Poincar\'e map to the NHIMs are deployed for
elucidating the dynamics in the neighbourhood of the saddle points. The
extended tidal tails, or tidal arms, formed by stars with low velocity which
escape through the Lagrange points are monitored. The numerical results of this
work are also compared with previous related work.
