  We calculate the magnetic phase diagram of the Hubbard model for a Bethe
lattice with nearest neighbour (NN) hopping $t_1$ and next nearest neighbour
(NNN) hopping $t_2$ in the limit of infinite coordination. We use the amplitude
$t_2/t_1$ of the NNN hopping to tune the density of states (DOS) of the
non-interacting system from a situation with particle-hole symmetry to an
asymmetric one with van-Hove singularities at the lower ($t_2/t_1>0$)
respectively upper ($t_2/t_1<0$) band edge for large enough $|t_2/t_1|$. For
this strongly asymmetric situation we find rather extended parameter regions
with ferromagnetic states and regions with antiferromagnetic states.
