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摘要: 给出相对论系统的Birkhoff函数和Birkhoff函数组、Pfaff作用量、PfaffBirkhoff原理、Birkhoff方程;研究相对论动力学系统的Birkhoff表示方法;根据在无限小变换下相对论Pfaff作用量的不变性和相对论Birkhoff方程的不变性,得到相对论Birkhoff系统的Noether对称性理论和Lie对称性理论;研究相对论Birkhoff系统的代数结构和Poisson积分方法.
Abstract: The Birkhoffian, the Birkhoff's functions, the Pfaff action, the Pfaff-Birkhoff principle and the Birkhoff equations of relativistic Birkhoff systems are given. The Birkhoff representation of relativistic dynamical systems is studied. Then the theory of Noether symmetries and Lie symmetries of the relativistic Birkhoff systems is obtained by the invariance of relativistic Pfaff action and relativistic Birkhoff equations under infinitesimal transformations. Finally the algebraic structure and Poisson integrals for the relativistic Birkhoff systems are studied.
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