We consider polygonal billiards and we show that every nonperiodic billiard trajectory hits a unique sequence of sides if all the holes of the polygonal table have non-zero minimal diameters, generalizing a classical theorem of Galperin, Krüger and Troubetzkoy. Our approach uses symbolic dynamics and elementary geometry. We review some classical constructions in polygonal billiards and we introduce, as one of our main tools, a method to code pairs of parallel billiard trajectories in non-simply connected polygons. We also discuss some useful properties of ‘generalized trajectories’, which can be uniquely constructed from the limits of converging sequences of billiard codings.

我们考虑多边形台球，并证明如果多边形台的所有孔的最小直径都不为零，则每个非周期性台球轨迹都会击中独特的边序列，从而推广了 Galperin、Krüger 和 Troubetzkoy 的经典定理。我们的方法使用符号动力学和基本几何。我们回顾了多边形台球中的一些经典结构，并介绍了一种在非简单连接多边形中对平行台球轨迹对进行编码的方法，作为我们的主要工具之一。我们还讨论了“广义轨迹”的一些有用特性，这些特性可以从台球编码收敛序列的限制中唯一地构造出来。