We consider a family of simple flows in tori that display chaotic behavior in a wide sense. But these flows do not have homoclinic nor heteroclinic orbits. They have only a fixed point which is of parabolic type. However, the dynamics returns infinitely many times near the fixed point due to quasi-periodicity. A preliminary example is given for maps introduced in a paper containing many examples of strange attractors in [6]. Recently, a family of maps similar to the flows considered here was studied in [9]. In the present paper we consider the case of 2D tori and the extension to tori of arbitrary finite dimension. Some other facts about exceptional frequencies and behavior around parabolic fixed points are also included.

中文翻译：

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Tori上的简单流，具有罕见的混乱

我们考虑了一系列简单的流在花托中的行为，这些流在广泛意义上表现出混乱的行为。但是这些流动没有同斜轨道或异斜轨道。它们只有一个抛物线型的固定点。但是，由于准周期，动力学在固定点附近无限多次返回。论文介绍的地图给出了一个初步的例子，其中包含[6]中许多奇怪的吸引子的例子。最近，在[9]中研究了一系列与此处考虑的流程相似的地图。在本文中，我们考虑二维托里的情况以及任意有限维的托里的扩展。还包括有关抛物线固定点周围异常频率和行为的其他一些事实。