Gradient-like flows on 3-manifolds. (English) Zbl 0822.57013
The author’s abstract: “We determine properties that a Lyapunov graph must satisfy for it to be associated with a gradient-like flow on a closed orientable 3-manifold. We also address the question of the realization of abstract Lyapunov graphs as gradient-like flows on 3- manifolds and as a byproduct, we prove a partial converse to the theorem which states the Morse inequalities for closed orientable 3-manifolds. We also present cancellation theorems of nondegenerate critical points for flows which arise as realizations of classical abstract Lyapunov graphs”.
Reviewer: Chang Kungching (Beijing)
MSC:
| 57N10 | Topology of general \(3\)-manifolds (MSC2010) |
| 37C10 | Dynamics induced by flows and semiflows |
| 37D15 | Morse-Smale systems |
Keywords:
Conley index; Lyapunov graph; gradient-like flow on a closed orientable 3-manifold; realization of abstract Lyapunov graphs; Morse inequalitiesReferences:
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