We consider a transitive uniformly quasi-conformal Anosov diffeomorphism [formula omitted] of a compact manifold [formula omitted]. We prove that if the stable and unstable distributions have dimensions greater than two, then [formula omitted] is [formula omitted] conjugate to an affine Anosov automorphism of a finite factor of a torus. If the dimensions are at least two, the same conclusion holds under the additional assumption that [formula omitted] is an infranilmanifold. We also describe necessary and sufficient conditions for smoothness of conjugacy between such a diffeomorphism and a small perturbation. AMS 2000 Mathematics subject classification: Primary 37C; 37D.
|Original language||English (US)|
|Number of pages||16|
|Journal||Journal of the Institute of Mathematics of Jussieu|
|State||Published - Oct 2003|
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