A geometric definition of the Mañé-Mather set and a Theorem of Marie-Claude Arnaud.

Patrick Bernard (1) , Joana Santos (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We study some properties of Lipschitz exact Lagrangian manifolds isotopic to the zero section. We prove that if such a manifold is invariant under an optical Hamiltonian, then it must be a Lipschitz graph. This extends a recent result of Marie-Claude Arnaud. We also obtain a new geometric description of the Mañé-Mather invariant set.

Domaines: Systèmes dynamiques [math.DS]

Patrick Bernard, Joana Santos. A geometric definition of the Mañé-Mather set and a Theorem of Marie-Claude Arnaud.. Mathematical Proceedings of the Cambridge Philosophical Society, 2012, 152 (1), pp.167-178. ⟨10.1017/S0305004111000685⟩. ⟨hal-00678709v1⟩