标题： Kowalevski陀螺仪在两个恒定场中的分岔图和临界子系统 显示英文标题

标题： Bifurcation diagrams and critical subsystems of the Kowalevski gyrostat in two constant fields

摘要： 科瓦列夫斯卡娅陀螺仪在两个恒定场中是唯一一个不可约化为更少维度系统的可积哈密顿系统，且仍具有明确的机械解释。 这种系统的实际显式积分很难通过现有技术获得。 因此，具有挑战性的问题变为基于相空间的Liouville叶层结构研究进行定性分析。 作为对该系统拓扑分析的第一种方法，我们找到了动量映射的分层临界集；该集合由频率数小于三的轨迹组成。 我们在三维空间中得到了分岔图的方程。 这些方程的形式便于对五维等能面上引起的分岔集进行分类。 显示英文摘要

摘要： The Kowalevski gyrostat in two constant fields is known as the unique example of an integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems in fewer dimensions and still having the clear mechanical interpretation. The practical explicit integration of this system can hardly be obtained by the existing techniques. Then the challenging problem becomes to fulfil the qualitative investigation based on the study of the Liouville foliation of the phase space. As the first approach to topological analysis of this system we find the stratified critical set of the momentum map; this set consists of the trajectories with number of frequencies less than three. We obtain the equations of the bifurcation diagram in three-dimensional space. These equations have the form convenient for the classification of the bifurcation sets induced on 5-dimensional iso-energetic levels.