  The dilatation of a pseudo-Anosov braid is a conjugacy invariant. In this
paper, we study the dilatation of a special family of pseudo-Anosov braids. We
prove an inductive formula to compute their dilatation, a monotonicity and an
asymptotic behavior of the dilatation for this family of braids. We also give
an example of a family of pseudo-Anosov braids with arbitrarily small
dilatation such that the mapping torus obtained from such braid has 2 cusps and
has an arbitrarily large volume.
