Structural classification and stability of divergence-free vector fields (Q696086)
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scientific article; zbMATH DE number 1799071
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Structural classification and stability of divergence-free vector fields |
scientific article; zbMATH DE number 1799071 |
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Structural classification and stability of divergence-free vector fields (English)
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10 September 2002
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The authors prove that a divergence-free vector field \(v\) on a two dimensional submanifold of \(S^2\) is structurally stable with divergence-free vector field perturbations if and only if (1) \(v\) is regular, (2) all interior saddle points of \(v\) are self-connected, and (3) each boundary saddle point is connected to boundary saddles on the same connected component of the boundary.
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divergence-free vector fields
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manifolds with boundary
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Poincaré-Bendixson theorem
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0.94659555
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0.90677935
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0.9005827
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0.89728093
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0.8920306
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0.8906721
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