位力定理框架内的恒星动力学：Ermakov-Lewis-Leach 不变量作为无穷守恒律级数的渐近小参数时间展开
Stellar dynamics within the virial theorem: asymptotic small-parameters time expansion of the Ermakov-Lewis-Leach invariant as an infinite series of conservation laws
AI总结：
本文提出对 Ermakov-Lewis-Leach 运动积分作渐近小参数展开，以无穷守恒律刻画位力化恒星系统，并在多种势模型与宇宙学场景中验证。
摘要：
本文在一种研究运动积分的新方法框架内，分析了表征位力化系统恒星动力学的无阻尼振荡机制。该方法具有宇宙学应用价值，因为它适用于从非高斯性时期到当代的宇宙演化任意阶段所需的计算。这里发展的新方法基于对 Ermakov-Lewis-Leach 运动积分新表达式的渐近小参数展开；由此产生的无穷系列新守恒律意味着新运动积分的存在性与唯一性；在将脉冲 Plummer 势、三个脉冲 Dehnen 势实例、脉冲谐和势、Jaffe 势、Hernquist 势应用于所研究问题之后，给出了解析示例。因此，复势的特殊情形也被纳入分析。由这些守恒律导出的运动常数被证明依赖于恒星系统的位力化半径和位力化质量，而与所采用的势无关。在一般的 Terzic'-Kandrup 势框架内给出了宇宙学实施。还提供了与数据分析技术的比较。
英文摘要：
The regime of undamped oscillations characterizing the stellar dynamics of virialised systems is analysed within the framework of a new approach to the study of the integrals of motion. The method is relevant as far as the cosmological implementation is concerned, as it applies to the calculations apt for any age of the evolution of the Universe starting from the epoch of non-Gaussianities until present time. The new method here developed is based on the asymptotic small-parameters expansion of the new expression of the Ermakov-Lewis-Leach integrals of motion; as a result, an infinite series of new conservation laws implies the uniqueness and existence of new integrals of motion; analytical examples are provided after the pulsed Plummer potential, the three instances of the pulsed Dehnen potentials, the pulsed harmonic potential, the Jaffe potential, the Hernquist potential, applied to the studied problem. Particular cases of complex potentials are therefore also comprehended in the analysis. The constants of motions descending from the conservation laws are demonstrated to depend on the virialised radius and on the virialised mass of the stellar system, independently of the potential used. Cosmological implementation is given within the framework of a generic Terzic'-Kandrup potential. Comparison with data analysis techniques are provided with.
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