On Uniformly Quasiconformal Anosov Systems

We show that for any uniformly quasiconformal symplectic Anosov diffeomorphism of a compact manifold of dimension at least 4, its finite cover is $C^\infty$ conjugate to an Anosov automorphism of a torus. We also prove that any uniformly quasiconformal contact Anosov flow on a compact manifold of dimension at least 5 is essentially $C^\infty$ conjugate to the geodesic flow of a manifold of constant negative curvature.

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Published 1 January 2005