| Type de publication : |
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Articles dans des revues avec comité de lecture |
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| Domaine : |
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Mathématiques/Systèmes dynamiques
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| Titre : |
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Square-tiled cyclic covers |
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| Auteur(s) : |
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Giovanni Forni, Carlos Matheus, Anton Zorich 1 |
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| Laboratoire : |
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| Résumé : |
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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. |
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Langue du texte
intégral : |
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Anglais |
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Date de production,
écriture : |
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24/07/2010 |
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| Journal : |
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JOURNAL OF MODERN DYNAMICS |
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| Audience : |
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internationale |
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| Date de publication : |
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2011 |
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| Volume : |
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5 |
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| Numéro : |
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2 |
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| Page, identifiant, ... : |
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285-318 |
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| Mots Clés : |
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Teichmuller geodesic flow – Kontsevich-Zorich cocycle – square-tiled surfaces |
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| Commentaire : |
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25 pages, 6 figures |
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