Three heteroclinic orbits induce a countable family of equivalence classes of regular flows
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914378557685760 |
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| author | Gurevich, Elena |
| author_facet | Gurevich, Elena |
| contents | 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 $γ\geq 3$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07470 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Three heteroclinic orbits induce a countable family of equivalence classes of regular flows Gurevich, Elena Dynamical Systems 37C15, 37C29, 37D15 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 $γ\geq 3$ 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. |
| title | Three heteroclinic orbits induce a countable family of equivalence classes of regular flows |
| topic | Dynamical Systems 37C15, 37C29, 37D15 |
| url | https://arxiv.org/abs/2603.07470 |