Pseudo-Anosov Mapping Classes and Their Representations by Products of Two Dehn Twists

Let ■ be a Riemann surface of analytically finite type(p,n) with 3p-3+n > 0.Let a ∈ S and S = ■ -{a}.In this article,the author studies those pseudo-Anosov maps on ■ that are isotopic to the identity on S and can be represented by products of Dehn twists.It is also proved that for any pseudo-Anosov map f of S isotopic to the identity on ■,there are infinitely many pseudo-Anosov maps F on S -{b} = ■ -{a,b},where b is a point on S,such that F is isotopic to f on S as b is filled in.