Abstract

A local version of the Fomenko conjecture on the possibility of the realization of the Liouville foliation with the Fomenko–Zieschang arbitrary topological invariant, which is a graph with numerical labels, by integrable billiards is discussed. It is proved that Liouville foliation with an arbitrary value of the integer mark which defines the Euler class of the Seifert manifold is algorithmically realized in the class of billiard books.

中文翻译：

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台球实现可积系统的赛弗特纤维数值不变性的实现

摘要

讨论了有关Fomenko猜想的局部版本，该问题通过可积分的台球实现了带有Fomenko-Zieschang任意拓扑不变量的Liouville插值的实现，Fomenko-Zieschang任意拓扑不变量是带有数字标签的图形。证明了在台球类中通过算法实现了具有定义Seifert流形的Euler类的整数标记的任意值的Liouville叶形成。