Pseudo-Anosov maps and simple closed curves on surfaces
  Given a pair of curves C_1 and C_2 on a hyperbolic surface F, when does there exist a pseudo-Anosov map sending one to another? More generally, one may ask the same question for C_i to be sets of disjoint simple closed curves. We will give necessary and sufficient conditions for the existence of such maps. 
Shicheng Wang, Ying-Qing Wu and Qing Zhou