The Lagrangian Conley Conjecture
Dynamical Systems
2010-12-07 v4 Symplectic Geometry
Abstract
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
@article{arxiv.0810.2108,
title = {The Lagrangian Conley Conjecture},
author = {Marco Mazzucchelli},
journal= {arXiv preprint arXiv:0810.2108},
year = {2010}
}
Comments
45 pages, 5 figures; final version, to appear in Commentarii Mathematici Helvetici