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arXiv · 2603.07470

Three heteroclinic orbits induce a countable family of equivalence classes of regular flows

Elena Gurevich
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Abstract

We solve the problem of topological classification for smooth structurally stable flows on closed four-dimensional manifolds, the non-wandering set of which contains exactly two saddle equilibria, and the wandering set contains isolated trajectories connecting these saddle equilibria (heteroclinic curves). In particular, we show that for a flow of the class under consideration on $\mathbb{CP}^2$, the number of heteroclinic curves is a complete topological invariant, while on the sphere $\mathbb S^4$, there exists a countably many equivalence classes with an arbitrary odd number $\gamma\geq 3$ of heteroclinic curves. These results contrast with a three-dimensional case, where under similar conditions there exists only finite set of equivalence classes for each number of heteroclinic curves.

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Elena Gurevich. 2026-03-08. Three heteroclinic orbits induce a countable family of equivalence classes of regular flows. https://arxiv.org/abs/2603.07470

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