Federico Rodriguez Hertz (Penn State U) - Rigidity for conjugacies of Anosov flows in dimension 3

In the 80's after work of Shub and Sullivan,
Feldman-Ornstein, de la Llave-Marco-Moriyon and Pollicott, it was
shown that if to Anosov flows are conjugated (time preserving orbit
equivalence) and corresponding Lyapunov exponents coincide, then the
flows are smoothly conjugated. In our work we show that in many cases,
the Lyapunov exponents condition is not needed, as it is already
implied by the existence of a topological conjugacy. In particular, we
show that the conjugacy is smooth, unless one of the flows is a
suspension, or the conjugacy swaps positive and negative SRB measures
of the two flows. This extends a recent work in the volume preserving
case. In this talk I will try to explain some of the features involved
in the proof. This is joint work with A. Gogolev and M. Leguil.