  In this article, we study the minimizing measures of the Tonelli
Hamiltonians. More precisely, we study the relationships between the so-called
Green bundles and various notions as: - the Lyapunov exponents of minimizing
measures; -the weak KAM solutions. In particular, we deduce that the support of
every minimizing measure all of whose Lyapunov exponents are zero is C1-regular
almost everywhere.
