On Anosov diffeomorphisms with asymptotically conformal periodic data

dc.creatorKalinin, Boris
dc.creatorSadovskaya, Victoria
dc.date2007-09-24
dc.date2008-03-29
dc.date.accessioned2026-07-07T09:28:53Z
dc.date.available2026-07-07T09:28:53Z
dc.descriptionWe 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.
dc.descriptionTo appear in Ergodic Theory and Dynamical Systems
dc.identifierhttps://arxiv.org/abs/0709.3790
dc.identifierhttp://arxiv.org/abs/0709.3790
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157588
dc.subjectDynamical Systems
dc.subject37C15; 37D20; 37D30
dc.titleOn Anosov diffeomorphisms with asymptotically conformal periodic data
dc.typetext

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