标题： 恒星动力学建模 -- 计数守恒量 显示英文标题

标题： Stellar Dynamical Modeling -- Counting Conserved Quantities

摘要： 了解星系恒星轨道所遵循的守恒量对于帮助我们理解星系内的恒星分布和结构非常重要。隔离运动积分和共振尤其重要，而非隔离积分则不那么重要。我们比较了两种计数守恒量的方法的行为和结果，一种基于相关积分方法，另一种是使用机器学习的较新方法。这两种方法都仅以相空间中的恒星轨道轨迹作为输入，我们从理论上的球形、轴对称和三轴模型星系中生成这些轨迹。这些轨道具有已知的隔离积分和共振。我们发现，这两种方法在恢复这些量的数量以及确定非隔离积分的数量方面都不完全有效。从计算机性能的角度来看，我们发现相关积分方法更快。由于缺乏适当的符号回归能力，从轨迹中确定（多个）守恒量的代数公式尚未成为可能。尽管我们指出了这些方法的不足之处，但它们可能作为轨迹分析工具包的一部分使用。 显示英文摘要

摘要： Knowing the conserved quantities that a galaxy's stellar orbits conform to is important in helping us understand the stellar distribution and structures within the galaxy. Isolating integrals of motion and resonances are particularly important, non-isolating integrals less so. We compare the behavior and results of two methods for counting the number of conserved quantities, one based on the correlation integral approach and the other a more recent method using machine learning. Both methods use stellar orbit trajectories in phase space as their only input, and we create such trajectories from theoretical spherical, axisymmetric and triaxial model galaxies. The orbits have known isolating integrals and resonances. We find that neither method is fully effective in recovering the numbers of these quantities, nor in determining the number of non-isolating integrals. From a computer performance perspective, we find the correlation integral approach to be the faster. Determining the algebraic formulae of (multiple) conserved quantities from the trajectories has not been possible due to the lack of an appropriate symbolic regression capability. Notwithstanding the shortcomings we have noted, it may be that the methods are usable as part of a trajectory analysis tool kit.