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| HAL : hal-00572334, version 2 |
| arXiv : 1103.0194 |
| DOI : 10.1017/S0143385712000065 |
| Fiche détaillée |  Récupérer au format |
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| Ergodic Theory and Dynamical Systems (2012) 1-20 |
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| Versions disponibles : | v1 (01-03-2011) | v2 (23-01-2012) |
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| Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of the Oseledet's splitting |
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| Marie-Claude Arnaud 1 |
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| (17/04/2012) |
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| We consider locally minimizing measures for the conservative twist maps of the $d$-dimensional annulus or for the Tonelli Hamiltonian flows defined on a cotangent bundle $T^*M$. For weakly hyperbolic such measures (i.e. measures with no zero Lyapunov exponents), we prove that the mean distance/angle between the stable and the unstable Oseledet's bundles gives an upper bound of the sum of the positive Lyapunov exponents and a lower bound of the smallest positive Lyapunov exponent. Some more precise results are proved too. |
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| 1 : | Laboratoire d'Analyse non linéaire et Géométrie (LANLG) |
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Université d'Avignon : EA2151 |
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| Domaine | : | Mathématiques/Systèmes dynamiques |
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| Lyapunov exponents – twist maps – green bundles – Tonelli Hamiltonians – Oseledet's splitting – minimizing measures |
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| hal-00572334, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00572334 | |
| oai:hal.archives-ouvertes.fr:hal-00572334 | |
| Contributeur : Marie-Claude Arnaud | |
| Soumis le : Lundi 23 Janvier 2012, 17:46:48 | |
| Dernière modification le : Jeudi 26 Avril 2012, 14:07:01 | |
