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ON LOCAL AND GLOBAL RIGIDITY OF QUASI-CONFORMAL ANOSOV DIFFEOMORPHISMS

Published online by Cambridge University Press:  16 September 2003

Boris Kalinin  and
Victoria Sadovskaya
Boris Kalinin
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA (kalinin@umich.edu; sadovska@umich.edu)
Victoria Sadovskaya
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA (kalinin@umich.edu; sadovska@umich.edu)
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Abstract

We consider a transitive uniformly quasi-conformal Anosov diffeomorphism $f$ of a compact manifold $\mathcal{M}$. We prove that if the stable and unstable distributions have dimensions greater than two, then $f$ is $C^\infty$ 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 $\mathcal{M}$ 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

Keywords

rigidityAnosov systemsconformal structuressmooth conjugacy
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 2 , Issue 4 , October 2003 , pp. 567 - 582
Copyright
2003 Cambridge University Press

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