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  • Критерий топологической сопряжённости многомерных градиентно-подобных потоков без гетероклинических пересечений на сфере

Article

Критерий топологической сопряжённости многомерных градиентно-подобных потоков без гетероклинических пересечений на сфере

In this article, we study gradient-like flows without heteroclinic intersections on an n-dimensional sphere, n>2, in sense of topological conjugacy. We prove that the class of topological conjugacy of such a flow is completely determined by the two-color tree corresponding to the skeleton formed by separatrices of codimension 1. In addition, we show that for such flows the concepts of topological equivalence and topological conjugacy coincide (which is completely wrong in the case of presence of limit cycles and connections)