论文标题
降低和集成性：几何视角
Reduction and integrability: a geometric perspective
论文作者
论文摘要
从现代角度开发了一种集成性和减少动力系统的几何方法。这种分析中的主要成分是在给定动力学下不变的无限对称性和张量场。特别强调了不变体积形式和相关的雅各比乘数理论，然后霍伊曼对称理论被开发为对Noether定理和非运动运动常数的补充。汉密尔顿 - 雅各比方程的几何方法被证明是在较低维歧管中搜索相关场的一个特定示例。
A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the infinitesimal symmetries and the tensor fields that are invariant under the given dynamics. Particular emphasis is given to the existence of invariant volume forms and the associated Jacobi multiplier theory, and then the Hojman symmetry theory is developed as a complement to Noether theorem and non-Noether constants of motion. The geometric approach to Hamilton-Jacobi equation is shown to be a particular example of the search for related field in a lower dimensional manifold.
