Explosion of differentiability for equivalencies between Anosov flows on 3-manifolds

Abstract

For Anosov flows obtained by suspensions of Anosov diffeomor- phisms on surfaces, we show the following type of rigidity result: if a topolog- ical conjugacy between them is differentiable at a point, then the conjugacy has a smooth extension to the suspended 3-manifold. This result generalizes the similar ones of Sullivan and Ferreira-Pinto for 1-dimensional expanding dynamics and also a result of Ferreira-Pinto for 2-dimensional hyperbolic dynamics.