Generalized Maupertuis’ principle with applications
Generalized Maupertuis’ principle with applications
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DOI：
10.1007/s10114-012-1001-7
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发表时间：
2012-03
期刊：
影响因子：
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通讯作者：
W. Cheng
中科院分区：
文献类型：
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作者：
W. Cheng
给出了Mañé的超临界势和最小作用对相关的Jacobi-Finsler度规的等价性的严格证明。因此，我们给出了一维机械系统的弱KAM解的显式表示，而不需要对哈密顿量的动能项作二次假设，并讨论了用Mather的α-函数的正则性假设来判定任意自由度系统的可积性结果的判据。
We give a rigorous proof of the equivalence of Mañé’s supercritical potential and the minimal action with respect to an associated Jacobi-Finsler metric. As a consequence, we give an explicit representation of the weak KAM solutions of one-dimensional mechanical systems without the quadratic assumption on the kinetic energy term of the Hamiltonians, and a criterion of the integrability result for such a system of arbitrary degree of freedom by the regularity assumption on Mather’sα-function is discussed.