  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.
