Tonelli拉格朗日系统的频率锁定
动力系统
2012-11-30 v2
摘要
我们证明，在二维构型空间上，对于一般的Tonelli拉格朗日系统，存在一个开稠密的上同调类子集，其Aubry集恰好由一个双曲周期轨道组成。
引用
@article{arxiv.1104.4226,
title = {Frequency locking for Tonelli Lagrangians},
author = {Daniel Massart},
journal= {arXiv preprint arXiv:1104.4226},
year = {2012}
}
备注
This paper has been withdrawn by the author due to a fatal flaw in the proof of the main results.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