 |
 |
|
|
| HAL : hal-00604368, version 1 |
| arXiv : 1007.4275 |
| Fiche détaillée |  Récupérer au format |
 |
| JOURNAL OF MODERN DYNAMICS 5, 2 (2011) 285-318 |
|
|
|
|
| Square-tiled cyclic covers |
|
|
| Giovanni ForniCarlos Matheus |
|
|
| (2011) |
|
|
|
| A cyclic cover of the projective plane branched at four points has a natural structure of a square-tiled surface. We describe the combinatorics of such a square-tiled surface, the geometry of the corresponding Teichmüller curve, and compute the Lyapunov exponents of the determinant bundle over the Teichmüller curve with respect to the geodesic flow. We find a new example of a Teichmüller curve with a completely degenerate Lyapunov spectrum (the only known example found previously by G. Forni also corresponds to a cyclic cover). Presumably, these two examples cover all possible Teichmüller curves with completely degenerate Lyapunov spectrum. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
|
|
|
CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
|
|
|
|
|
|
|
|
|
| Domaine | : | Mathématiques/Systèmes dynamiques |
|
|
| Teichmuller geodesic flow – Kontsevich-Zorich cocycle – square-tiled surfaces |
|
|
|
| Lien vers le texte intégral : |
|
| http://fr.arXiv.org/abs/1007.4275 |
| hal-00604368, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00604368 | |
| oai:hal.archives-ouvertes.fr:hal-00604368 | |
| Contributeur : Marie-Annick Guillemer | |
| Soumis le : Mardi 28 Juin 2011, 17:24:01 | |
| Dernière modification le : Jeudi 25 Août 2011, 15:35:26 | |
