ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

9. Ordinary Differential Equations and Dynamical Systems

1991 MS Classification: 58Fxx Massart, Daniel, Universität Freiburg On the convexity of the action of a Lagrangian Let M be a smooth compact manifold, and let L be a Lagrangian on M, i. e. a function on T M which is convex and superlinear in the fibers. We study the convexity of Mather’s α-function on H^{1}(M, ℝ) in terms of the relative Čhech homology of a special set of minimising trajectories, called Peierls set after A. Fathi.