相空间中离散力学系统对称性的摄动与Hojman型绝热不变量

Perturbation of symmetries and Hojman adiabatic invariants of discrete mechanical systems in the phase space

研究相空间中离散力学系统对称性的摄动与绝热不变量.列出相空间中未受扰离散力学系统的特殊Lie对称性导致的Hojman型精确不变量.基于相空间中力学系统的高阶绝热不变量的定义,研究在小扰动作用下系统Lie对称性的摄动,得到了相空间中离散力学系统的一类新的绝热不变量——Hojman型绝热不变量.举例说明结果的应用.

The perturbation of symmetries and adiabatic invariants of discrete mechanical systems in the phase space are studied. The Hojman exact invariants introduced by the special Lie symmetries of discrete mechanical systems in the phase space without perturbation are given. Based on the definition of high-order adiabatic invariants of a mechanical system in the phase space, the perturbation of Lie symmetries of the system by the action of small disturbance is investigated, and a type of new adiabatic invariants of the system are obtained, which can be called the Hojman adiabatic invariants. An example is given to illustrate the application of the results.