**iModèles hyperboliques des flots topologiques d’Anosov transtitifs.**Hyperbolic models of transitive topological Anosov flows.

A topological Anosov flow on a closed 3-manifold is a non-singular flow that resembles very much a smooth Anosov flow: It is expansive and satisfies the (global) shadowing property. Moreover, it preserves a pair of transverse sta- ble/unstable foliations that intersect along the orbits of the flow. The main difference with a (smooth) Anosov flow is the lack of a global uniformly hyper- bolic structure.

We investigate the question of weather or not every topological Anosov flow in a 3-manifold is, actually, orbit equivalent with some smooth Anosov flow. Apart from its own theoretical interest, this question appears related with some techniques for the construction of Anosov flows on 3-manifolds, notably with the so called Fried surgery.

Our work consists in show that, under the hypothesis of transitivity, every topological Anosov flow is orbitally equivalent with a smooth Anosov flow.

In this talk we are going to present the main ideas and difficulties behind the construction of these smooth hyperbolic models associated with transitive topological Anosov flows. As well, we will give a flavour of how this study can be reduced to pseudo-Anosov dynamics on surfaces with boundary.