论文标题
Lipschitz的亚行动，用于本地最大双曲线套件的$ C^1 $流动
Lipschitz sub-actions for locally maximal hyperbolic sets of a $C^1$ flow
论文作者
论文摘要
Livšic theorem for flows asserts that a Lipschitz observable that has zero mean average along every periodic orbit is necessarily a coboundary, that is the Lie derivative of a Lipschitz function smooth along the flow direction. The positive Livšic theorem bounds from below the observable by such a coboundary as soon as the mean average along every periodic orbit is non negative.以前的证据给出了Höldercoboundary。假设动力学是由局部最大双曲线流给出的，我们表明可以是Lipschitz。我们介绍了一种新工具：受Fathi弱KAM理论的启发的Lax-Oleinik Semigroup。
Livšic theorem for flows asserts that a Lipschitz observable that has zero mean average along every periodic orbit is necessarily a coboundary, that is the Lie derivative of a Lipschitz function smooth along the flow direction. The positive Livšic theorem bounds from below the observable by such a coboundary as soon as the mean average along every periodic orbit is non negative. Previous proofs give a Hölder coboundary. Assuming that the dynamics is given by a locally maximal hyperbolic flow, we show that the coboundary can be Lipschitz. We introduce a new tool: the Lax-Oleinik semigroup, inspired by Fathi's weak KAM theory.
