两个常量域中Kowalevski陀螺体的分岔图和临界子系统
Bifurcation diagrams and critical subsystems of the Kowalevski gyrostat in two constant fields
摘要：
两个常量域中的Kowalevski陀螺体是三自由度可积哈密顿系统的一个特例，它不能简化为一族维数更少的系统，而且仍具有清晰的力学解释。用现有的方法很难得到该系统的显式积分。因此，如何在研究相空间的Liouville叶理的基础上进行定性研究就成为一个具有挑战性的问题。作为拓扑分析的第一种方法，我们发现分层的临界集的动量映射，这个集合由轨道的频率数小于3。得到了三维空间中的分岔图方程。这些方程具有便于对5维等能能级上诱导的分岔集进行分类的形式。
英文摘要：
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.
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