Abstract

Integrals of motion are constructed from noncommutative (NC ) Kepler dynamics, generating \(\mathrm{SO}(3)\), \(\mathrm{SO}(4)\), and \(\mathrm{SO}(1,3)\) dynamical symmetry groups. The Hamiltonian vector field is derived in action–angle coordinates, and the existence of a hierarchy of bi-Hamiltonian structures is highlighted. Then, a family of Nijenhuis recursion operators is computed and discussed.

中文翻译：

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非对易开普勒动力学：对称群和双哈密顿结构

摘要

运动积分由非对易 (NC) 开普勒动力学构建，生成\(\mathrm{SO}(3)\)、\(\mathrm{SO}(4)\)和\(\mathrm{SO}(1) ,3)\)动态对称群。哈密​​顿向量场是在动作角坐标中导出的，并且强调了双哈密顿结构的层次结构的存在。然后，计算和讨论了一系列 Nijenhuis 递归算子。