Generalizations of the Bonatti-Langevin example of Anosov flow and their classification up to topological equivalence (Q1281361)

The author considers the problem of topological equivalence between Anosov flows. How much do the topological properties of the ambient manifold influence on the dynamical properties of the flow? The author gives a complete classification of Anosov flows on certain 3-manifolds up to topological equivalence. These manifolds are the orientable ones obtained by gluing the nontrivial circle bundle over the two-punctured projective plane along its two boundary components. Moreover, the author presents (apparently) the first known examples of 3-manifolds admitting at the same time \(R\)-covered and non \(R\)-covered Anosov flows.