The space of projective measured foliations is (one of) the boundaries of Teichmuller space. One can consider a special subclass of this set that define Teichmuller geodesics whose projection to moduli space is contained in a fixed compact set. These can be thought of as analogous to badly approximable rotations. The main result of the talk is that this set is path connected in high enough genus. This is joint work with Sebastian Hensel.