2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142481The 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.20 pages, 13 figuresGeometric TopologyDynamical Systems37E30, 57M27 (Primary) 57M50 (Secondary)text