Geometry/Dynamical Systems Seminar

In this talk I shall sketch a proof of the following result: on a closed configuration space M, the Euler-Lagrange system associated to any time-periodic Tonelli Lagrangian function L : R/Z x TM --> R admits infinitely many periodic solutions. More precisely, I will show that there are infinitely many contractible periodic orbits with a priori bounded mean action and either infinitely many of them are 1-periodic or their basic period is unbounded.