Minimal pseudo-Anosov translation lengths on the Teichmuller space

This thesis is a study of the asymptotic behavior of minimal pseudo-Anosov translation lengths on the Teichmuller space. For tori with n marked points, we find an upper bound for the minimal pseudo-Anosov translation length. The upper bound is on the order of 1/|??(S)| . We find similar asymptotics for genus g surfaces with n marked points as g and n vary in certain prescribed ways. However, for a surface S with fixed genus g ??? 2 and varied n, we prove that the asymptotic behavior (in n) is different. The main result of this thesis is that the least pseudo-Anosov translation length shrinks to zero on the order of log |??(S)|/|??(S)| as |??(S)| ??? ???. This is in contrast with the previously-known results for the cases of closed surfaces and marked spheres, in which the behavior is on the order of 1/|??(S)| . These results are published in [Tsa09]