(1) Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany;(2) Division of Engineering and Applied Science, California Institute of Technology, 90025 Pasadena, CA, USA
Abstract:
Summary For a simple class of Lagrangians and variational integrators, derived by time discretization of the action functional, we establish (i) the Γ-convergence of the discrete action sum to the action functional; (ii) the relation between Γ-convergence and weak* convergence of the discrete trajectories in {itW{su1,℞}}({ofR};{ofr{sun}; and (iii) the relation between Γ-convergence and the convergence of the Fourier transform of the discrete trajectories as measured in the flat norm.
