具有Lie和Noether点对称性的自治三维牛顿系统
Autonomous three dimensional Newtonian systems which admit Lie and Noether point symmetries
摘要：
确定了具有Lie点对称性的三维自治Newton系统和具有Noether点对称性的三维自治Newton Hamilton系统。我们应用的结果，以确定二维哈密顿动力系统，在一个空间中的常数非零曲率和可积通过Noether点对称。结果的推导是几何的，可以自然地扩展到更高的维度。
英文摘要：
We determine the autonomous three dimensional Newtonian systems which admit Lie point symmetries and the three dimensional autonomous Newtonian Hamiltonian systems, which admit Noether point symmetries. We apply the results in order to determine the two dimensional Hamiltonian dynamical systems which move in a space of constant non-vanishing curvature and are integrable via Noether point symmetries. The derivation of the results is geometric and can be extended naturally to higher dimensions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
