  We study magnetic flux interacting with arrays of pinning sites (APS) placed
on vertices of hyperbolic tesselations (HT). We show that, due to the gradient
in the density of pinning sites, HT APS are capable of trapping vortices for a
broad range of applied magnetic fluxes. Thus, the penetration of magnetic field
in HT APS is essentially different from the usual scenario predicted by the
Bean model. We demonstrate that, due to the enhanced asymmetry of the surface
barrier for vortex entry and exit, this HT APS could be used as a "capacitor"
to store magnetic flux.
