We consider dynamics of a scalar piecewise linear "saw map" with infinitely many linear segments. In particular, such maps are generated as a Poincar\'e map of simple two-dimensional discrete time piecewise linear systems involving a saturation function. Alternatively, these systems can be viewed as a feedback loop with the so-called stop hysteresis operator. We analyze chaotic sets and attractors of the "saw map" depending on its parameters.

翻译：我们考虑的是带有无限多线性段的标语线性“锯图”的动态。特别是,这些地图的生成方式是包含饱和功能的简单二维离散时间线性系统的波因卡图。或者,这些系统可以被视为与所谓的歇歇斯底里操作员的反馈循环。我们根据“锯图”的参数分析混乱的数据集和吸引器。