  We study particle motion in rotating saddle-shaped potentials. It is known
that such rotating potentials can generate bounded motion for particles with a
parabolic dispersion law through the combination of potential, centrifugal and
Coriolis forces in the rotating frame. When applied to massless Dirac
particles, for example electrons in graphene, such a potential is shown to lead
to eigenstates that are spatially localized near the center of the saddle at
certain energies. Although other states also exist at these energies, they have
non-overlapping support in the oscillator basis, which tend to give the
localized states a substantial life-time also when imperfections are present.
