JournalscmhVol. 86, No. 1pp. 189–246

The Lagrangian Conley conjecture

  • Marco Mazzucchelli

    Université de Lyon, France
The Lagrangian Conley conjecture cover


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 (2010), no. 1, pp. 189–246

DOI 10.4171/CMH/222