The Lagrangian Conley conjecture

Marco Mazzucchelli (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

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.

Domaines: Mathématiques [math]

Marco Mazzucchelli. The Lagrangian Conley conjecture. Commentarii Mathematici Helvetici, 2011, pp.189 - 246. ⟨10.4171/CMH/222⟩. ⟨ensl-01404041⟩