Title: On the connections between symmetries and conservation rules of dynamical systems Show Chinese title

Title: 关于动力系统对称性与守恒定律之间的联系

Abstract: The strict connection between Lie point-symmetries of a dynamical system and its constants of motion is discussed and emphasized, through old and new results. It is shown in particular how the knowledge of a symmetry of a dynamical system can allow to obtain conserved quantities which are invariant under the symmetry. In the case of Hamiltonian dynamical systems it is shown that, if the system admits a symmetry of "weaker" type (specifically, a \lambda\ or a \Lambda-symmetry), then the generating function of the symmetry is not a conserved quantity, but the deviation from the exact conservation is "controlled" in a well defined way. Several examples illustrate the various aspects. Show Chinese abstract

Abstract: 该动力系统与其运动常数之间的严格联系通过旧的和新的结果进行了讨论和强调。特别展示了如何利用动力系统的对称性来获得在该对称性下不变的守恒量。在哈密顿动力系统的情况下，如果系统具有“较弱”类型的对称性（具体来说，是\lambda 或\Lambda -对称性），则该对称性的生成函数不是守恒量，但其偏离精确守恒的方式是被明确控制的。多个例子说明了各个方面的内容。