Abstract
In this paper, the problem of topological classification of gradient-like flows without heteroclinic intersections, given on a four-dimensional projective-like manifold, is solved. We show that a complete topological invariant for such flows is a bi-color graph that describes the mutual arrangement of closures of three-dimensional invariant manifolds of saddle equilibrium states. The problem of construction of a canonical representative in each topological equivalence class is solved.
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