ON SYMMETRY AND INVARIANT OF DYNAMICAL SYSTEMS
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摘要: 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。Abstract: 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.
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Key words:
- dynamical system /
- invariant /
- symmetry /
- differential manifold /
- form calculus
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