Generic properties and problems of minimizing measures of Lagrangian systems
Generic properties and problems of minimizing measures of Lagrangian systems
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DOI：
10.1088/0951-7715/9/2/002
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发表时间：
1996-03
期刊：
影响因子：
1.7
通讯作者：
R. Mãné
中科院分区：
文献类型：
--
作者：
R. Mãné
本文证明了拉格朗日流的极小化测度是不变的，且拉格朗日量在其遍历分量的支集上与一个常数上同调。此外，它表明，通用拉格朗日有一个独特的最小化措施，这是唯一的遍历，是一个限制的不变概率的拉格朗日流的周期轨道上支持。
It is proved here that minimizing measures of a Lagrangian flow are invariant and the Lagrangian is cohomologous to a constant on the support of their ergodic components. Moreover, it is shown that generic Lagrangians have a unique minimizing measure which is uniquely ergodic and is a limit of invariant probabilities supported on periodic orbits of the Lagrangian flows.