Abstract

A local version of A.T. Fomenko’s conjecture on modeling of integrable systems by billiards is formulated. It is proved that billiard systems realize arbitrary numerical marks of Fomenko–Zieschang invariants. Thus, numerical marks are not a priori a topological obstacle to the realization of the Liouville foliation of integrable systems by billiards.

中文翻译：

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台球可积系统的拓扑建模：数值不变量的实现

摘要

制定了AT Fomenko的关于台球可积分系统建模的猜想的本地版本。事实证明，台球系统可以实现Fomenko–Zieschang不变量的任意数字标记。因此，数字标记并不是先验台球实现可积系统的Liouville叶面的拓扑障碍。