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A pseudo-Anosov flow on a closed 3-manifold dynamically represents a face F of the Thurston norm ball if the cone on F is dual to the cone spanned by homology classes of closed orbits of the flow. Fried showed that for every fibered face of the Thurston norm ball there is a unique, up to isotopy and reparameterization, flow which dynamically represents the face.  Mosher found sufficient conditions on a non-circular flow to dynamically represent a non-fibered face, but the problem of the existence and uniqueness of the flow for every non-fibered face was unresolved.

I will outline how to show that a non-fibered face can be in fact dynamically represented by multiple topologically inequivalent flows, and discuss how two distinct flows representing the same face may be related.