# On the Multiplicity of Periodic Orbits for Tonelli Systems

 GEOMETRY/DYNAMICAL SYSTEMS SEMINAR Topic: On the Multiplicity of Periodic Orbits for Tonelli Systems Speaker: Marco Mazzucchelli Affiliation: Max Planck Institute for Mathematics, Leipzig, Germany Date: Tuesday, April 20 Time/Room: 4:30pm - 5:30pm/S-101

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.