We prove a Lagrangian analogue of the Conley conjecture: given a 1-periodic
Tonelli Lagrangian with global flow on a closed configuration space, the
associated Euler-Lagrange system has infinitely many periodic solutions. More
precisely, we show that there exist infinitely many contractible integer
periodic solutions with a priori bounded mean action and either infinitely many
of them are 1-periodic or they have unbounded period.Comment: 45 pages, 5 figures; final version, to appear in Commentarii
Mathematici Helvetic
