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We consider locally minimizing measures for the conservative twist maps ofthe $d$-dimensional annulus or for the Tonelli Hamiltonian flows defined on acotangent bundle $T^*M$. For weakly hyperbolic such measures (i.e. measureswith no zero Lyapunov exponents), we prove that the mean distance/angle betweenthe stable and the unstable Oseledet's bundles gives an upper bound of the sumof the positive Lyapunov exponents and a lower bound of the smallest positiveLyapunov exponent. Some more precise results are proved too.

ergodic theory and dynamical systems/ergodic theory and dynamical systems

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