Classification of Morse-Smale vector fields on 2-manifolds. (Ukrainian. English summary) Zbl 1091.57015
Summary: We consider the minimal Morse-Smale fields on a closed oriented 2-manifold. By means of chord diagrams we give necessary and sufficient conditions for topological equivalence of these fields. We also calculate the number of topologically non-equivalent fields on a pretzel.
MSC:
| 57N05 | Topology of the Euclidean \(2\)-space, \(2\)-manifolds (MSC2010) |
| 57R25 | Vector fields, frame fields in differential topology |
| 37D15 | Morse-Smale systems |
| 37C10 | Dynamics induced by flows and semiflows |
| 37C15 | Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems |
