Title: Stellar dynamics within the virial theorem: asymptotic small-parameters time expansion of the Ermakov-Lewis-Leach invariant as an infinite series of conservation laws Show Chinese title

Title: 在virial定理框架下的恒星动力学：Ermakov-Lewis-Leach不变量的渐近小参数时间展开作为无穷守恒律序列

Abstract: 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. Show Chinese abstract

Abstract: 在研究运动积分的新方法框架内，分析了表征致密化系统恒星动力学的无阻尼振荡规律。 该方法在宇宙学实现方面具有相关性，因为它适用于从非高斯时期到现今宇宙演化任意阶段的计算。 这里提出的新方法基于 Ermakov-Lewis-Leach 运动积分新表达式的渐近小参数展开；结果表明，无穷级数的新守恒定律意味着存在新的运动积分，且这些积分是唯一的；在脉冲 Plummer 势、三种脉冲 Dehnen 势、脉冲谐波势、Jaffe 势和 Hernquist 势应用于所研究的问题后，提供了解析例子。 因此，复杂势的特殊情况也包含在分析中。 由守恒定律得出的动力常数被证明取决于恒星系统的致密化半径和致密化质量，而与所使用的势无关。 在通用 Terzic'-Kandrup 势的框架内给出了宇宙学实现。 还提供了与数据分析技术的比较。