A topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics
A topological classification of billiards in locally planar domains bounded by arcs of confocal quadrics
复制标题
以共焦二次曲面为界的局部平面域中台球的拓扑分类
DOI：
10.1070/sm2015v206n10abeh004502
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
V. V. Fokicheva
中科院分区：
文献类型：
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作者：
V. V. Fokicheva
发现了一类新的可积台球系统，称为广义台球。这些台球是通过将经典的台球域沿着它们的边界粘合而形成的域中的台球。(经典台球区域是由共焦二次曲面的圆弧限定的平面的一部分。)基于可积系统的Fomeko-Zieschang不变量理论，得到了广义台球的一个完全拓扑分类，达到了Liouville等价。参考书目：18种。
A new class of integrable billiard systems, called generalized billiards, is discovered. These are billiards in domains formed by gluing classical billiard domains along pieces of their boundaries. (A classical billiard domain is a part of the plane bounded by arcs of confocal quadrics.) On the basis of the Fomenko-Zieschang theory of invariants of integrable systems, a full topological classification of generalized billiards is obtained, up to Liouville equivalence. Bibliography: 18 titles.