### Séminaire Gaston Darboux

Le vendredi 21 janvier 2011 à 11:15 - salle 431

Marco Mazzucchelli
On the multiplicity of periodic orbits for Tonelli systems

In this talk I shall sketch a proof of the following result: on a closed configuration space, the Euler-Lagrange system associated to any time-periodic Tonelli Lagrangian function 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.

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