Generalized Maupertuis’ principle with applications |
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基金项目: | Supported by the National Basic Research Program of China (Grant No. 2007CB814800) and Natural Scientific Foundation of China (Grant No. 10971093) |
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摘 要: | We give a rigorous proof of the equivalence of Ma'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's α-function is discussed.
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关 键 词: | Generalized Maupertuis’ principle weak KAM solutions α-function |
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