关于力学系统的对称性与不变量

ON SYMMETRY AND INVARIANT OF DYNAMICAL SYSTEMS

本文综述了近10年来关于力学系统的对称性和不变量的研究所提出的新概念、新理论,主要包括经典Noether对称性的微分几何描述、高阶Noether对称性、Lie对称性,拟对称性和伴随对称性以及与之相应的不变量,关于非保守系统的高阶Noether对称性和Lie对称性的结果属首次公布。

In this paper, we review the research results published in recent ten years on symmetry and invariant of dynamical systems, including generalized Noether symmetries, higher-order Noether symmetries, Lie symmetries, pseudo-symmetries and adjoint symmetries. We also present here for the first time our research results on higher-order Noether symmetries and Lic symmetries for nonconscrvative dynamical systems.