Lagrangian flows: The dynamics of globally minimizing orbits
Lagrangian flows: The dynamics of globally minimizing orbits
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DOI：
10.1007/bf01233389
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发表时间：
1997-09
期刊：
影响因子：
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通讯作者：
R. Mãné
中科院分区：
文献类型：
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作者：
R. Mãné
本文的目的是给出关于闭流形上欧拉-拉格朗日方程某些特解的一些结果，这些结果将在即将发表的一篇文章中得到证明。我们的主要结果推广到了时间相关的周期拉格朗日函数，我们选择自治的情况是因为这个形式上更简单的框架可以更容易地达到我们的概念和结果的核心。此外，自治情况显示出某些特殊特征，涉及能量作为第一积分，值得特别注意。它们与Carneiro[C]发现的能量与Mather的作用函数[Ma]之间的联系密切相关。
The objective of this note is to present some results, to be proved in a forthcoming paper, about certain special solutions of the Euler-Lagrange equations on closed manifolds. Our main results extend to time dependent periodic Lagrangians with minor modifications.We have chosen the autonomous case because this formally simpler framework allows to reach more easily the core of our concepts and results. Moreover the autonomous case exhibits certain special features involving the energy as a first integral that deserve special attention. They are closely related to the link found by Carneiro [C] between the energy and Mather's action function [Ma].