Smooth rigidity of uniformly quasiconformal Anosov flows

Yong Fang (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We classify quasiconformal Anosov flows whose strong stable and unstable distributions are at least two dimensional and the sum of these two distributions is smooth. We deduce from this classification result the complete classification of volume-preserving quasiconformal diffeomorphisms whose stable and unstable distributions are at least two dimensional. Our central idea is to take a good time change so that perodic orbits are equi-distributed with respect to a lebesgue measure.

Mots clés: Anosov flows; Anosov diffeomorphisms; Bowen-Margulis measure; entropy

Domaines: Systèmes dynamiques [math.DS]

Yong Fang. Smooth rigidity of uniformly quasiconformal Anosov flows. Ergodic Theory and Dynamical Systems, 2004, 24, pp.1937-1959. ⟨hal-00004410⟩