Mise en position optimale de tores par rapport à un flot d'Anosov

Let Φ′ be an Anosov flow on a (non atoroidal) 3-manifoldM. We say that an incompressible torusT embedded inM admits an optimal position with respect to Φ′ if it is isotopic to a torus transverse to Φ′ outside a finite number of periodic orbits contained inT (there's an additional condition we dont's mention here). The first remark is that such an optimal position is quasi unique, i.e., we prove that if two tori in optimal position are homotopics inM, then they are homotopics along the flow. Then we give some sufficient condition for a torus admiting an optimal position. Eventually, we show that if a finite collection of disjoint tori is such that each torus admits an optimal position, then these optimal positions can be chosen disjoints one from each other.