Jan Philipp Schröder

Global minimizers for Tonelli Lagrangians on the 2-torus

We study action-minimizing orbits in Tonelli Lagrangian systems on the 2-torus on fixed energy levels above Manes strict critical value. Our work generalizes the results of Morse, Hedlund and Bangert on minimal geodesics in Riemannian 2-tori. The techniques in the proofs involve classical variational ones, as well as the theories of Mather, Mane and Fathi, which allow the step from reversible to non-reversible dynamics.