论文标题
$ h^2 $的可整合动力学通过耦合摩尔斯和罗森 - 莫尔斯电势产生
Superintegrable dynamics on $H^2$ generated by coupling the Morse and Rosen-Morse potentials
论文作者
论文摘要
分析了通过耦合摩尔斯和罗森 - 摩尔斯电势在二维双曲平面上定义的哈密顿动力学。证明，如果参数$ \ tilde的乘积是摩尔斯电位的$ \ tilde的乘积，并且曲率绝对值的平方根是一个合理的数字，则所有有界运动的轨道都关闭。通过明确构造多项式运动的运动，可以证实相当于最大可促进性的轨迹的这种特性。
A Hamiltonian dynamics defined on the two-dimensional hyperbolic plane by coupling the Morse and Rosen-Morse potentials is analyzed. It is demonstrated that orbits of all bounded motions are closed iff the product of the parameter $\tilde a$ of the Morse potential and the square root of the absolute value of the curvature is a rational number. This property of trajectories equivalent to the maximal superintegrability is confirmed by explicit construction of polynomial superconstant of motion.
