论文标题
riemannian覆盖物上变量和可及性的分离
Separation of Variables and Superintegrability on Riemannian Coverings
论文作者
论文摘要
我们在覆盖歧管$ m_k $上介绍了stäckel可分离坐标，其中$ k $是一个有理参数，具有某些恒定狂热的riemannian歧管，并具有扭曲的歧管结构。这些覆盖歧管在文献中隐含着与与多项式的可整合系统有关的文献中，在任意高度的Momenta第一个积分中，例如Tremblay-Turbiner-Winternitz系统。我们在这里首次在这里学习天然哈密顿系统在这些流形上的多雌性和可共性，并查看这些属性如何依赖于参数$ k $。
We introduce Stäckel separable coordinates on the covering manifolds $M_k$, where $k$ is a rational parameter, of certain constant-curvature Riemannian manifolds with the structure of warped manifold. These covering manifolds appear implicitly in literature as connected with superintegrable systems with polynomial in the momenta first integrals of arbitrarily high degree, such as the Tremblay-Turbiner-Winternitz system. We study here for the first time multiseparability and superintegrability of natural Hamiltonian systems on these manifolds and see how these properties depend on the parameter $k$.
