We denote by δ
g (resp. δ
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 δ
g for
g ≡ 0,1,5,6,7,9 (mod 10), δ
g+ for
g ≡ 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.
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