Commentarii Mathematici Helvetici

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Volume 86, Issue 1, 2011, pp. 189–246
DOI: 10.4171/CMH/222

Published online: 2010-12-05

The Lagrangian Conley conjecture

Marco Mazzucchelli[1]

(1) Université de Lyon, France

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.

Keywords: Lagrangian dynamics, Morse theory, periodic orbits, Conley conjecture

Mazzucchelli Marco: The Lagrangian Conley conjecture. Comment. Math. Helv. 86 (2011), 189-246. doi: 10.4171/CMH/222