In this paper, we consider regular topological flows on closed \(n\)-manifolds. Such flows have a hyperbolic (in the topological sense) chain recurrent set consisting of a finite number of fixed points and periodic orbits. The class of such flows includes, for example, Morse – Smale flows, which are closely related to the topology of the supporting manifold. This connection is provided by the existence of the Morse – Bott energy function for the Morse – Smale flows. It is well known that, starting from dimension 4, there exist nonsmoothing topological manifolds, on which dynamical systems can be considered only in a continuous category. The existence of continuous analogs of regular flows on any topological manifolds is an open question, as is the existence of energy functions for such flows. In this paper, we study the dynamics of regular topological flows, investigate the topology of the embedding and the asymptotic behavior of invariant manifolds of fixed points and periodic orbits. The main result is the construction of the Morse – Bott energy function for such flows, which ensures their close connection with the topology of the ambient manifold.

在本文中，我们考虑封闭\(n\)上的规则拓扑流-歧管。这种流有一个双曲线（在拓扑意义上）链循环集，由有限数量的不动点和周期轨道组成。例如，此类流包括 Morse-Smale 流，它与支持流形的拓扑结构密切相关。这种联系是由 Morse-Smale 流的 Morse-Bott 能量函数的存在提供的。众所周知，从第 4 维开始，存在非光滑拓扑流形，其上的动力系统只能在连续范畴内考虑。任何拓扑流形上规则流的连续类似物的存在是一个悬而未决的问题，对于这种流的能量函数的存在也是如此。在本文中，我们研究了规则拓扑流的动力学，研究嵌入的拓扑结构和不动点和周期轨道的不变流形的渐近行为。主要结果是为此类流构建 Morse-Bott 能量函数，确保它们与环境流形的拓扑结构紧密连接。