We consider the two body problem with central interaction on two point homogeneous spaces from point of view of the invariant differential operators theory. The representation of the two particle Hamiltonian in terms of the radial differential operator and invariant operators on the symmetry group is found. The connection of different mass center definitions for these spaces to the obtained expression for Hamiltonian operator is studied.
Hyperbolic Center of Mass for a System of Particles on a two-dimensional Space with Constant Negative Curvature: An Application to the Curved $2$- and $3$-Body Problems
本文给出了二维常负高斯曲率曲面上质点系的\textit{ center of mass}的一个简单表达式。利用几何的基本技巧，得到了内禀坐标的表达式，并说明了它是如何扩展欧几里德情形的定义的。这个论证是有建设性的，也可用于定义一维双曲空间$\mathbb{L}^1_R$上的质点系的质心。最后，给出了它在$2$ -和$3$ -曲面问题中的应用.
Local Density Approximation and Other Limit Regimes for a Homogeneous Bose Gas with Repulsive Three-Body Interactions in Low-Dimensional Space
Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam（胡志明市科学大学数学与计算机科学学院）；Vietnam National University, Ho Chi Minh City, Vietnam（胡志明市越南国立大学）；Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam（胡志明市栋塔大学数学与统计学院）
Nonplanar Periodic Solutions for Spatial Restricted 3-Body and 4-Body Problems
本文研究了以下空间限制性三体和四体问题非平面周期解的存在性：对于$N=2 or 3$，给定任意质量$m_{1},...,m_{N}$，$m_{1},...,m_{N}$的质点在以质心为中心的$N$圆轨道上运动，足够小的质量在通过质心的垂直轴上运动.利用变分极小化方法，我们建立了反T/2或奇对称环空间上拉格朗日作用的极小元的存在性。利用局部极小的Jacobi必要条件，证明了这些极小解是非平面周期解。
