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Integrable billiard systems realize toric foliations on lens spaces and the 3-torus
Sbornik: Mathematics ( IF 0.8 ) Pub Date : 2020-04-19 , DOI: 10.1070/sm9189
V. V. Vedyushkina 1
Affiliation  

An integrable billiard system on a book, a complex of several billiard sheets glued together along the common spine, is considered. Each sheet is a planar domain bounded by arcs of confocal quadrics; it is known that a billiard in such a domain is integrable. In a number of interesting special cases of such billiards the Fomenko-Zieschang invariants of Liouville equivalence (marked molecules ##IMG## [http://ej.iop.org/images/1064-5616/211/2/201/MSB_211_2_201ieqn1.gif] {$W^*$} ) turn out to describe nontrivial toric foliations on lens spaces and on the 3-torus, which are isoenergy manifolds for these billiards. Bibliography: 18 titles.

中文翻译:

集成式台球系统可实现晶状体空间和3-torus的复曲面叶

考虑一本书上的可集成台球系统,即沿着共同的脊线粘合在一起的几张台球板的复合体。每张纸都是一个由共焦二次曲面弧界定的平面区域;众所周知,在这种领域中的台球是可整合的。在此类台球的许多有趣的特殊情况下,Liouville等价的Fomenko-Zieschang不变量(标记的分子## IMG ## [http://ej.iop.org/images/1064-5616/211/2/201/MSB_211_2_201ieqn1 .gif] {$ W ^ * $})描述了晶状体空间和3-torus上非平凡的复曲面叶面,这是这些台球的等能量流形。参考书目:18种。
更新日期:2020-04-19
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