  We reveal the escape mechanism of orbits in a Hamiltonian system with four
exit channels composed of two-dimensional perturbed harmonic oscillators. We
distinguish between trapped chaotic, non-escaping regular and escaping orbits
by conducting a thorough and systematic numerical investigation in both the
configuration and the phase space. We locate the different basins of escape and
we relate them withe the corresponding escape times of orbits. The SALI method
is used for determining the ordered or chaotic nature of the orbits. It was
observed that trapped and non-escaping orbits coexist with several escape
basins. When the energy is very close to the escape energy the escape rate of
orbits is huge, while as the value of the energy increases the orbits escape
more quickly to infinity. Furthermore, initial conditions of orbits located
near the boundaries of the basins of escape and also in the vicinity of the
fractal domains were found to posses the largest escape rates. The degree of
the fractality of the phase space was calculated as a function of the value of
the energy. Our results were compared with earlier related work.
