Abstract: The Nielsen-Thurston
theorem states that a non-periodic orientation preserving homeomorphism of a
Riemann surface is isotopic to either a reducible map or a pseudo-Anosov map. A
basic question is how we can determine a given homeomorphism of S is a pseudo-Anosov map. Thurston obtained a set of pseudo-Anosov maps as products of
Dehn twists along filling simple closed geodesics. Consider a Riemann surface S
that has at least one puncture a. It
is well known that there exists a family of pseudo-Anosov maps on S
isotopic to the identity on In this paper, we construct a new
family of pseudo-Anosov maps on S by products of elements of and
