In this paper, we obtain a classification of gradient-like flows on arbitrary surfaces by generalizing the circular Fleitas scheme. In 1975 he proved that such a scheme is a complete invariant of topological equivalence for polar flows on 2- and 3-manifolds. In this paper, we generalize the concept of a circular scheme to arbitrary gradient-like flows on surfaces. We prove that the isomorphism class of such schemes is a complete invariant of topological equivalence. We also solve exhaustively the realization problem by describing an abstract circular scheme and the process of realizing a gradient-like flow on the surface. In addition, we construct an efficient algorithm for distinguishing the isomorphism of circular schemes.

在本文中，我们通过推广圆形 Fleitas 方案获得了任意表面上的类梯度流的分类。1975 年，他证明了这样的方案是 2 流形和 3 流形上的极流拓扑等价的完全不变量。在本文中，我们将圆形方案的概念推广到表面上的任意梯度状流动。我们证明了此类方案的同构类是拓扑等价的完全不变量。我们还通过描述抽象的圆形方案和在表面上实现类梯度流的过程，详尽地解决了实现问题。此外，我们构建了一种有效的算法来区分循环方案的同构。