双力场中Kovalevskaya陀螺运动问题的奇点分类
Classification of singularities in the problem of motion of the Kovalevskaya top in a double force field
摘要：
研究了Kovalevskaya顶在双重力场中的运动问题（A.G. Reyman和M.A. Semenov-Tian-Shansky（无陀螺动量）。它是一个具有三个自由度的完全可积的哈密顿系统，不能简化为具有两个自由度的系统族。研究了积分映射的临界集。描述了临界子系统和分岔图。给出了所有非退化临界点的分类。这些点的集合由平衡点（秩为0的非退化奇点）、奇异周期运动（秩为1的非退化奇点）以及临界双频运动（秩为2的非退化奇点）组成。
英文摘要：
The problem of motion of the Kovalevskaya top in a double force field is investigated (the integrable case of A.G. Reyman and M.A. Semenov-Tian-Shansky without a gyrostatic momentum). It is a completely integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems with two degrees of freedom. The critical set of the integral map is studied. The critical subsystems and bifurcation diagrams are described. The classification of all nondegenerate critical points is given. The set of these points consists of equilibria (nondegenerate singularities of rank 0), of singular periodic motions (nondegenerate singularities of rank 1), and also of critical two-frequency motions (nondegenerate singularities of rank 2).
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