On Anosov diffeomorphisms with asymptotically conformal periodic data

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We consider transitive Anosov diffeomorphisms for which every periodic orbit has only one positive and one negative Lyapunov exponent. We establish various properties of such systems including strong pinching, C^{1+β} smoothness of the Anosov splitting, and C^1 smoothness of measurable invariant conformal structures and distributions. We apply these results to volume preserving diffeomorphisms with two-dimensional stable and unstable distributions and diagonalizable derivatives of the return maps at periodic points. We show that a finite cover of such a diffeomorphism is smoothly conjugate to an Anosov automorphism of a torus. As a corollary we obtain local rigidity for such diffeomorphisms. We also establish a local rigidity result for Anosov diffeomorphisms in dimension three.
To appear in Ergodic Theory and Dynamical Systems

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Dynamical Systems, 37C15; 37D20; 37D30

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http://salesiana.dossiersoluciones.com/handle/123456789/157588

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0709.3790
 http://arxiv.org/abs/0709.3790

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arXiv