In this paper we provide a construction which produces sequences of pseudo-Anosov mapping classes on surfaces with decreasing Euler characteristic. The construction is based on Penner's examples used in the proof that the minimal dilatation, δg,0, for a closed surface of genus g behaves asymptotically like (1/g). We give a bound for the dilatation of the pseudo-Anosov elements of each sequence produced by the construction and use this bound to show that if gi=rni for some rational number r0 then δgi,ni behaves like (1/|ϗ(Sgi,ni)|) where ϗ(Sgi,ni) is the Euler characteristic of the genus gi surface with ni punctures.
展开▼
