https://hal-univ-avignon.archives-ouvertes.fr/hal-01065120Arnaud, Marie-ClaudeMarie-ClaudeArnaudLMA - EA2151 Laboratoire de Mathématiques d'Avignon - AU - Avignon UniversitéLyapunov exponents of minimizing measures for globally positive diffeomorphisms in all dimensionsHAL CCSD2016discrete weak KAM theorysymplectic twist mapsLyapunov exponentsAubry-Mather theoryminimizing measuresGreen bundles[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Arnaud, Marie-ClaudeBlanc - Hamilton-Jacobi et théorie KAM faible : à l'interface des EDP, systèmes dynamiques lagrangiens et symboliques - - KAMFAIBLE2007 - ANR-07-BLAN-0361 - BLANC - VALID - 2014-09-17 21:18:542022-02-22 11:36:032014-09-18 08:14:42enJournal articleshttps://hal-univ-avignon.archives-ouvertes.fr/hal-01065120/documentapplication/pdf1The globally positive diffeomorphisms of the 2n-dimensional annulus are important because they represent what happens close to a completely elliptic periodic point of a symplectic diffeomorphism where the torsion is positive definite. For these globally positive diffeomorphisms, an Aubry-Mather theory was developed by Garibaldi & Thieullen that provides the existence of some minimizing measures. Using the two Green bundles G- and G+ that can be defined along the support of these minimizing measures, we will prove that there is a deep link between: -the angle between G- and G+ along the support of the considered measure m; -the size of the smallest positive Lyapunov exponent of m; -the tangent cone to the support of m.