Consider a billiard in a plane domain bounded by confocal ellipses and hyperbolae. A Hooke potential acts on a point mass. This dynamical systems turns out to be completely Liouville integrable. A topological analysis of the Liouville foliation of isoenergy manifolds at all possible levels of the Hamiltonian is performed and the complete Fomenko- Zieschang invariants (marked molecules) of these manifolds are constructed. Bibliography: 15 titles.

中文翻译：

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势场中以共焦二次曲面为界的台球的拓扑分析

考虑以共焦椭圆和双曲线为界的平面域中的台球。胡克势作用于点质量。事实证明，这个动力系统完全是刘维尔可积的。对哈密顿量所有可能水平的等能流形的 Liouville 叶理进行拓扑分析，并构建这些流形的完整 Fomenko-Zieschang 不变量（标记分子）。参考书目：15个标题。