  We show that the presence of KAM islands in nonhyperbolic chaotic scattering
has deep implications on the unpredictability of open Hamiltonian systems. When
the energy of the system increases the particles escape faster. For this reason
the boundary of the exit basins becomes thinner and less fractal. Hence, we
could expect a monotonous decrease in the unpredictability as well as in the
fractal dimension. However, within the nonhyperbolic regime, fluctuations in
the basin entropy have been uncovered. The reason is that when increasing the
energy, both the size and geometry of the KAM islands undergo abrupt changes.
These fluctuations do not appear within the hyperbolic regime. Hence, the
fluctuations in the basin entropy allow us to ascertain the hyperbolic or
nonhyperbolic nature of a system. In this manuscript we have used continuous
and discrete open Hamiltonian systems in order to show the relevant role of the
KAM islands on the unpredictability, and the utility of the basin entropy to
analyze this kind of systems.
