论文标题
球体，椭圆形和双曲线
Integrable systems on the sphere, ellipsoid and hyperboloid
论文作者
论文摘要
欧几里得空间中的仿射变换在$ r^n $中嵌入的球形束，椭圆形和倍boloid骨之间产生了对应关系的对应关系。使用此对应关系和合适的耦合常数转换，我们可以在肉体机构情况下以实际运动积分在球体情况下获得真正的运动积分。我们讨论了一些与不变的系统，这些系统具有分数，四分之一的多项式。
Affine transformations in Euclidean space generates a correspondence between integrable systems on cotangent bundles to the sphere, ellipsoid and hyperboloid embedded in $R^n$. Using this correspondence and the suitable coupling constant transformations we can get real integrals of motion in the hyperboloid case starting with real integrals of motion in the sphere case. We discuss a few such integrable systems with invariants which are cubic, quartic and sextic polynomials in momenta.
