Billiards are considered in compact domains on a Minkowski plane whose boundary consists of arcs of confocal quadrics with angles at corner points ##IMG## [http://ej.iop.org/images/1064-5616/211/1/1/MSB_211_1_1ieqn1.gif] {$\leqslant\pi/2$} . A classification is obtained for these billiards, called simple billiards. The first integrals and trajectories of the motion of a ball in simple billiards are described. The Fomenko-Zieschang invariants are calculated for every simple billiard, and a theorem is proved which shows that only three different Liouville foliations of simple billiards exist on the Minkowski plane. Bibliography: 23 titles.

中文翻译：

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台球由Minkowski平面上的共焦二次曲面弧界定

台球在Minkowski平面上的紧致区域中考虑，该平面的边界由共焦二次曲面的弧组成，这些二次曲面在角点处具有角度## IMG ## [http://ej.iop.org/images/1064-5616/211/1/1 /MSB_211_1_1ieqn1.gif] {$ \ leqslant \ pi / 2 $}。获得了这些台球的分类，称为简单台球。描述了简单台球中球的运动的第一积分和轨迹。为每个简单的台球计算Fomenko-Zieschang不变量，并证明了一个定理，该定理表明在Minkowski平面上仅存在三种不同的简单台球的Liouville叶面。参考书目：23种。