Generalized Maupertuis' Principle with Applications  

作　　者：Wei CHENG 

机构地区：[1]Department of Mathematics,Nanjing University

出　　处：《Acta Mathematica Sinica,English Series》2012年第11期2153-2160,共8页数学学报（英文版）

基　　金：Supported by the National Basic Research Program of China (Grant No. 2007CB814800);Natural Scientific Foundation of China (Grant No. 10971093)

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.

关 键 词：Generalized Maupertuis＇ principle weak KAM solutions a-function 

分 类 号：O186.12[理学—数学]