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On the rigidity of quasiconformal Anosov flows

Published online by Cambridge University Press:  01 December 2007

YONG FANG
YONG FANG*
Affiliation:
Département de Mathématiques, Université de Cergy-Pontoise, avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France (email: yfang@math.u-cergy.fr)
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Abstract

We 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, orbit equivalent either to the suspension of a symplectic hyperbolic automorphism of a torus or to the geodesic flow of a closed hyperbolic manifold.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 27 , Issue 6 , December 2007 , pp. 1773 - 1802
Copyright
Copyright © Cambridge University Press 2007

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