  In this letter we study how hyperbolic and non hyperbolic regions in the
neighborhood of a resonant island perform a important role allowing or
forbidding stickiness phenomenon around islands in conservative systems. The
vicinity of the island is composed by non hyperbolic areas that almost prevent
the trajectory to visit the island edge. For some specific parameters there are
tiny channels embedded in the non hyperbolic area that are associated to
hyperbolic fixed points present in the neighborhood of the islands. Such
channels allow the trajectory to be injected in the inner portion of the
vicinity. When the trajectory crosses the barrier imposed by the non hyperbolic
regions, it spends a long time to abandon the surrounding of the island, since
the barrier also prevents the trajectory to scape from the neighborhood of the
island. In this scenario the non hyperbolic structures are the responsible for
the stickiness phenomena, and more than that, the strength of the sticky
effect. We reveal that those properties of the phase space allow us to
manipulate the existence of extreme events (and the transport associated to it)
responsible for the non equilibrium fluctuation of the system. In fact we
demonstrate that monitoring very small portions of the phase space (namely
$\approx 4\times 10^{-4}$ \% of it) it is possible to generate a completely
diffusive system eliminating long time recurrences that result from the
stickiness phenomenon.
