On the indices of singular points for planar bounded piecewise smooth polynomial vector field
We prove that for any piecewise-smooth bounded polynomial vector field in R2 with finitely many finite H-singular points (which include singular points, hyperbolic pseudo-equilibria and two fold singularities), the sum of the indices of all its finite H-singular points is 1.
| Authors: | , , |
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| Format: | article |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:281994 |
| Online Access: | https://ddd.uab.cat/record/281994 https://dx.doi.org/urn:doi:10.1016/j.nahs.2023.101350 |
| Access Level: | Open access |
| Keyword: | Bounded vector field Index of singular points Piecewise smooth polynomial vector field Stereographic projection |
| Summary: | We prove that for any piecewise-smooth bounded polynomial vector field in R2 with finitely many finite H-singular points (which include singular points, hyperbolic pseudo-equilibria and two fold singularities), the sum of the indices of all its finite H-singular points is 1. |
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