  The escape mechanism of the four hill potential is explored. A thorough
numerical investigation takes place in several types of two-dimensional planes
and also in a three-dimensional subspace of the entire four-dimensional phase
space in order to distinguish between bounded (ordered and chaotic) and
escaping orbits. The determination of the location of the basins of escape
toward the different escape channels and their correlations with the
corresponding escape time of the orbits is undoubtedly an issue of paramount
importance. It was found that in all examined cases all initial conditions
correspond to escaping orbits, while there is no numerical indication of stable
bounded motion, apart from some isolated unstable periodic orbits. Furthermore,
we monitor how the fractality evolves when the total orbital energy varies. The
larger escape periods have been measured for orbits with initial conditions in
the fractal basin boundaries, while the lowest escape rates belong to orbits
with initial conditions inside the basins of escape. We hope that our numerical
analysis will be useful for a further understanding of the escape dynamics of
orbits in open Hamiltonian systems with two degrees of freedom.
