Teichmüller geodesics that do not have a limit in $\mathcal{PMF}$

Abstract

We construct a Teichmüller geodesic which does not have a limit on the Thurston boundary of the Teichmüller space. We also show that for this construction the limit set is contained in a one-dimensional simplex in $\mathcal{P}\mathcal{ℳ}\mathcal{ℱ}$.