标题： 三维非退化开普勒库仑势的三元泊松代数 显示英文标题

标题： Ternary Poisson algebra for the non degenerate three dimensional Kepler Coulomb potential

摘要： 在三维平直空间中，任何具有五个功能独立运动积分的经典哈密顿量，包括哈密顿量本身，都被称为超可积的。 Kalnins、Kress 和 Miller 证明了，在非退化势的情况下，即依赖于四个参数的线性势，具有二次对称性，会有一个第六个二次积分，该积分与其他积分线性无关。 这个第六个积分的存在意味着运动积分形成一个具有五个生成元的二元类似费米子的二次泊松代数。 由 Verrier 和 Evans 引入的开普勒库仑势是超可积系统的一个特例，其中除了其余的二次积分外，还有两个四阶的独立积分。 相应的积分泊松代数是一个二次代数，具有与具有二次积分系统的非退化情况相同的特殊形式。 显示英文摘要

摘要： In the three dimensional flat space any classical Hamiltonian, which has five functionally independent integrals of motion, including the Hamiltonian, is characterized as superintegrable. Kalnins, Kress and Miller have proved that, in the case of non degenerate potentials, i.e potentials depending linearly on four parameters, with quadratic symmetries, posses a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral imply that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. The Kepler Coulomb potential that was introduced by Verrier and Evans is a special case of superintegrable system, having two independent integrals of motion of fourth order among the remaining quadratic ones. The corresponding Poisson algebra of integrals is a quadratic one, having the same special form, characteristic to the non degenerate case of systems with quadratic integrals.