Frequency locking for Tonelli Lagrangians
Dynamical Systems
2012-11-30 v2
Abstract
We prove that for a generic Tonelli Lagrangian on a configuration space of dimension two, there exists an open dense subset of cohomology classes, whose Aubry set consists of exactly one hyperbolic periodic orbit.
Cite
@article{arxiv.1104.4226,
title = {Frequency locking for Tonelli Lagrangians},
author = {Daniel Massart},
journal= {arXiv preprint arXiv:1104.4226},
year = {2012}
}
Comments
This paper has been withdrawn by the author due to a fatal flaw in the proof of the main results. Actually the error comes from the reference [Mt03]. In Theorem 1 of said reference an equality is claimed in the case where the base manifold is a closed, oriented surface. The proof of this equality uses a result by Boyland and Gol\'e. This result is incorrectly cited