On the rigidity of quasiconformal Anosov flows

Abstract

AbstractWe develop further our study of quasiconformal Anosov flows in our previous (Y. Fang. Smooth rigidity of uniformly quasiconformal Anosov flows. Ergod. Th. & Dynam. Sys.24 (2004), 1–23). For example, we prove the following result: Let φ be a transversely symplectic Anosov flow with dim  Ess≥2 and dim  Esu≥2. If φ is quasiconformal, then it is, up to finite covers, $C^\infty $ orbit equivalent either to the suspension of a symplectic hyperbolic automorphism of a torus or to the geodesic flow of a closed hyperbolic manifold.