INFINITELY MANY EVEN PERIODIC SOLUTIONS OF LAGRANGIAN SYSTEMS ON ANY RIEMANNIAN TORI WITH EVEN POTENTIAL IN TIME.

In this paper, we prove that the Lagrangian system on any Riemannian torus with C3-smooth even and τ-periodic potential in time possesses infinitely many different periodic contractible even solutions with integer multiple periods of τ. As a consequence, we get that the same conclusion holds for any τ > 0 and the Lagrangian system on any Riemannian torus with C3-smooth potential independent of time. [ABSTRACT FROM AUTHOR]