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

Let S be a Riemann surface of analytically finite type (p, n) with 3p-3+n > 0. Let a ∈ (～S) and S = (～S) - {a}. In this article, the author studies those pseudo-Anosov maps on S 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 S, there are infinitely many pseudo-Anosov maps F on S - {b} = (～S) - {a, b}, where b is a point on S, such that F is isotopic to f on S as b is filled in.