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.
Cite this article
Marco Mazzucchelli, The Lagrangian Conley conjecture. Comment. Math. Helv. 86 (2011), no. 1, pp. 189–246DOI 10.4171/CMH/222