Green bundles, Lyapunov exponents and regularity along the supports of the minimizing measures.

M.-C Arnaud (1)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon

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 μ, all of whose Lyapunov exponents are zero, is C 1-regular μ-almost everywhere. Résumé Dans cet article, on étudie les mesures minimisantes de Hamiltoniens de Tonelli. Plus précisément, on explique quelles relations existent entre les fibrés de Green et différentes notions comme :

Domaines: Mathématiques [math]

M.-C Arnaud. Green bundles, Lyapunov exponents and regularity along the supports of the minimizing measures.. Annales de l'Institut Henri Poincaré, 2012, ⟨10.1016/j.anihpc.2012.04.007⟩. ⟨hal-01325834⟩