On Anosov diffeomorphisms with asymptotically conformal periodic data
| dc.creator | Kalinin, Boris | |
| dc.creator | Sadovskaya, Victoria | |
| dc.date | 2007-09-24 | |
| dc.date | 2008-03-29 | |
| dc.date.accessioned | 2026-07-07T09:28:53Z | |
| dc.date.available | 2026-07-07T09:28:53Z | |
| dc.description | 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. | |
| dc.description | To appear in Ergodic Theory and Dynamical Systems | |
| dc.identifier | https://arxiv.org/abs/0709.3790 | |
| dc.identifier | http://arxiv.org/abs/0709.3790 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/157588 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37C15; 37D20; 37D30 | |
| dc.title | On Anosov diffeomorphisms with asymptotically conformal periodic data | |
| dc.type | text |