Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of the Oseledet's splitting

Abstract : 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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Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2012, pp.1-20. 〈10.1017/S0143385712000065〉
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Contributeur : Marie-Claude Arnaud <>
Soumis le : lundi 23 janvier 2012 - 17:46:48
Dernière modification le : lundi 21 mars 2016 - 17:35:09
Document(s) archivé(s) le : mardi 24 avril 2012 - 02:26:51

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Marie-Claude Arnaud. Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of the Oseledet's splitting. Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2012, pp.1-20. 〈10.1017/S0143385712000065〉. 〈hal-00572334v2〉

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