Description of bifurcations and symmetries of integrable systems is an important branch of geometry that has many applications. Important results have been obtained recently in the descriptions of bifurcations of integrable billiards and in modelling of Hamiltonian systems of mechanics and dynamics by billiards. The paper contains interesting problems, as well as a research program for the near future. In the closing of the paper, the results allowing one to describe hidden symmetries of Hamiltonian bifurcations are given as an example of a work close to billiards subject.

中文翻译：

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台球和几何和物理的可集成性。新范围和新潜力

可积系统的分叉和对称性的描述是几何学的一个重要分支，具有许多应用。最近在可积分台球的分叉的描述以及台球的力学和动力学的哈密顿系统建模中获得了重要的结果。该论文包含有趣的问题，以及近期的研究计划。在本文的结尾，给出了一个结果来描述哈密顿分叉的隐藏对称性，作为一个接近台球主题的例子。