一般动力学系统的精确不变量和绝热不变量

在增广相空间中研究一般动力学系统的精确不变量与绝热不变量，建立了该空间中力学系统的对称性与不变量之间的关系，提出了一般动力学系统的高阶绝热不变量的概念及其构造方法，揭示了高阶绝热不变量与无穷小对称变换之间的正反关系，讨论了ＶａｎｄｅｒＰｏｌ方程和Ｄｕｆｆｉｎｇ－ＶａｎｄｅｒＰｏｌ方程的一阶绝热不变量与相应的无穷小对称变换．

EXACT INVARIANT AND ADIABATIC INVARIANT OF A GENERAL DYNAMICAL SYSTEM

This paper studies the exact invariant and the adiabatic invariant of a general dynamical system in the extended phase space and gives the relation between the symmetry and the invariant of the system in the space.It presents the conception and a structure method of the higher order adiabatic invariant for the system,reveals the relation between the higher order adiabatic invariant and the infinitesimal symmetric transformations and discusses the first order adiabatic invariant and corresponding infinitesimal symmetric transformations for the Van der Pol equation and the Duffing-Van der Pol equation.