This paper concerns the set
of pseudo-Anosovs which occur as monodromies of fibrations on manifolds obtained from the
magic –manifold
by Dehn filling three cusps with a mild restriction. Let
be the manifold obtained
from by Dehn filling one
cusp along the slope .
We prove that for each
(resp. ), the
minimum among dilatations of elements (resp. elements with orientable invariant foliations) of
defined on a closed
surface of genus
is achieved by the monodromy
of some –bundle over the
circle obtained from
or by
Dehn filling both cusps. These minimizers are the same ones identified by
Hironaka, Aaber and Dunfield, Kin and Takasawa independently. In the case
we find a new family of pseudo-Anosovs defined on
with orientable invariant foliations obtained from
or
by Dehn filling both
cusps. We prove that if
is the minimal dilatation of pseudo-Anosovs with orientable invariant foliations defined
on ,
then
where
is the minimal dilatation of pseudo-Anosovs on an
–punctured
disk. We also study monodromies of fibrations on
. We prove
that if
is the minimal dilatation of pseudo-Anosovs on a genus
surface
with
punctures, then