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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

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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https://hal.archives-ouvertes.fr/hal-00572334
Contributor : Marie-Claude Arnaud <>
Submitted on : Monday, January 23, 2012 - 5:46:48 PM
Last modification on : Tuesday, December 8, 2020 - 10:18:58 AM
Long-term archiving on: : Tuesday, April 24, 2012 - 2:26:51 AM

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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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