The Lagrangian Conley Conjecture

Details The Lagrangian Conley Conjecture The Lagrangian Conley Conjecture

2008-10-12

arxiv.org/abs/0810.2108v4

Commentarii Mathematici Helvetici 86 (2011), no. 1, 189-246

Mathematics

Dynamical Systems

45 pages, 5 figures; final version, to appear in Commentarii Mathematici Helvetici

Scientific paper

10.4171/CMH/222

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.

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