EXPLOSION OF DIFFERENTIABILITY FOR EQUIVALENCIES BETWEEN ANOSOV FLOWS ON 3-MANIFOLDS

Abstract

For Anosov flows obtained by suspensions of Anosov diffeomorphisms on surfaces, we show the following type of rigidity result: if a topological 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.