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.

Bibliographic Details
Authors: Li, Shimin|||0000-0003-1695-0097, Llibre, Jaume|||0000-0002-9511-5999, Sun, Xianbo
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
Description
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.