ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 58F05 Iturriaga, Renato, G. Contreras, G. Paternain and M. Paternain Lagrangian Graphs, Minimizing Measures and Mañe’s Critical Values Title Lagrangian Graphs, Minimizing Measures and Mañe’s Critical Values Joint work with G. Contreras, G. Paternain and M. Paternain Section Number: 9 Ordinary Differential Equations and Dynamical Systems Mathematics Subject Classification:58F05 Abstract: Let L be a convex superlinear Lagrangian on a closed connected manifold N. We show that the critical value, as defined by Mañé, of the lift of L to a covering of N equals the infimum of the values of k such that the energy level k bounds an exact Lagrangian graph in the cotangent bundle of the covering. Also that if the Lagranian flow of L on the energy level k is Anosov, then k must be bigger than the critical value c_{u}(L) of the lift of L to the universal covering of N. Finally we show the existence of weak KAM solutions for coverings of N and we explain the relationship between Fathi’s results and Mañé’s action potentials.