  The main result of this paper is a universal finiteness theorem for the set
of all small dilatation pseudo-Anosov homeomorphisms, ranging over all
surfaces. More precisely, we consider pseudo-Anosovs F:S to S with |chi(S)|
log(lambda(F)) bounded above by some constant, and we prove that, after
puncturing the surfaces at the singular points of the stable foliations, the
resulting set of mapping tori is finite. Said differently, there is a finite
set of fibered hyperbolic 3-manifolds so that all small dilatation
pseudo-Anosovs occur as the monodromy of a Dehn filling on one of the
3-manifolds in the finite list, where the filling is on the boundary slope of a
fiber.
