Aubry sets vs Mather sets in two degrees of freedom
arXiv:0803.2647 · doi:10.1007/s00526-011-0393-z
Abstract
We study autonomous Tonelli Lagrangians on closed surfaces. We aim to clarify the relationship between the Aubry set and the Mather set, when the latter consists of periodic orbits which are not fixed points. Our main result says that in that case the Aubry set and the Mather set almost always coincide.
Revised and expanded version. New proof of Lemma 2.3 (formerly Lemma 14)