hal-00572334, version 1
Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of the Oseledet's splitting
(2011-03-01)
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.
- 1:
- Université d'Avignon : EA2151
- Domain : Mathematics/Dynamical Systems
- Keywords : Lyapunov exponents – twist maps – green bundles – Tonelli Hamiltonians – Oseledet's splitting – minimizing measures
- Available versions : v1 (2011-03-01) v2 (2012-01-23)
- hal-00572334, version 1
- http://hal.archives-ouvertes.fr/hal-00572334
- oai:hal.archives-ouvertes.fr:hal-00572334
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- Submitted on: Tuesday, 1 March 2011 11:30:36
- Updated on: Tuesday, 1 March 2011 16:15:23
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