摘要
We give a rigorous proof of the equivalence of Manes 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 a- function is discussed.
We give a rigorous proof of the equivalence of Manes 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 a- function is discussed.
基金
Supported by the National Basic Research Program of China (Grant No. 2007CB814800)
Natural Scientific Foundation of China (Grant No. 10971093)
