Abstract

The local case of A. Fomenko conjecture on the possibility of modeling Liouville foliations by integrable billiards is discussed. An extended version of its statements on numerical invariants on the edge of the Fomenko–Zieschang invariant of the Liouville foliation is proved. We show the realization of the Liouville foliation with some combinations of numerical mark values on a fixed edge by an appropriate class of integrable billiards.

中文翻译：

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台球对 Liouville Foliations 的局部建模：边缘不变量的实现

摘要

讨论了通过可积台球模拟 Liouville 叶理的可能性的 A. Fomenko 猜想的局部案例。证明了其关于 Liouville 叶理的 Fomenko-Zieschang 不变量边缘上的数值不变量的陈述的扩展版本。我们通过适当类别的可积台球展示了在固定边缘上具有一些数字标记值组合的 Liouville foliation。