Pseudo-Anosovs on closed surfaces having small entropy and the Whitehead sister link exterior

We denote by delta(g) (resp. delta(+)(g)), the minimal dilatation for pseudo-Anosovs (resp. pseudo-Anosovs with orientable invariant foliations) on a closed surface of genus g. This paper concerns the pseudo-Anosovs which occur as monodromies of fibrations on manifolds obtained from the Whitehead sister link exterior W by Dehn filling two cusps, where the fillings are on the boundary slopes of fibers of W. We give upper bounds of delta(g) for g equivalent to 0, 1, 5, 6, 7, 9 (mod 10), delta(+)(g) for g equivalent to 1, 5, 7, 9 (mod 10). Our bounds improve the previous one given by Hironaka. We note that the monodromies of fibrations on W were also studied by Aaber and Dunfield independently.