The axes in Tp

We show that there is a one-to-one natural correspondence between the axes in the Teichmüller space Tp (p > 1) and finite unions of finite sets (modulo a Fuchsian group) on the boundary of the unit disk. As a corollary to this result we obtain a new proof of Thurstonʹs theorem that there is exactly one axis in Tp which is invariant under a hyperbolic modular transformation.