Vertices of Mather's beta function
Vertices of Mather's beta function
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DOI：
10.1017/s0143385704000835
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发表时间：
2005-05
影响因子：
0.9
通讯作者：
O. Osuna
中科院分区：
文献类型：
--
作者：
O. Osuna
给定一个拉格朗日L，马瑟引入了L的$\beta$-函数，它是一个凸函数。欧拉-拉格朗日流的许多有趣的性质可以从研究$\beta$-函数的行为中推导出来。在这项工作中，我们获得了$\beta$-函数的顶点与相关不变测度的Hausdorff维之间的一些联系，从中我们恢复了$\beta$-函数的可微性的结果。
Given a Lagrangian L, Mather introduced the $\beta$-function of L, which is a convex function. Many interesting properties of the Euler–Lagrange flow can be derived from the study of the behaviour of the $\beta$-function. In this work we obtain some links between the vertices of the $\beta$-function and the Hausdorff dimension of the associated invariant measures, from which we recover a result of differentiability of the $\beta$-function.