Stable Strata of Geodesics in Outer Space

In this paper we propose an Outer space analogue for the principal stratum of the unit tangent bundle to the Teichm"uller space $\mathcal{T}(S)$ of a closed hyperbolic surface $S$. More specifically, we focus on properties of the geodesics in Teichm"uller space determined by the principal stratum. We show that the analogous Outer space “principal” periodic geodesics share certain stability properties with the principal stratum geodesics of Teichm"uller space. We also show that the stratification of periodic geodesics in Outer space exhibits some new pathological phenomena not present in the Teichm"uller space context.