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On the indices of singular points for planar bounded piecewise smooth polynomial vector field / Li, Shimin (Hangzhou Normal University. School of Mathematics) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Sun, Xianbo (Hangzhou Normal University. School of Mathematics)
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.
2023 - 10.1016/j.nahs.2023.101350
Nonlinear Analysis: Hybrid Systems, Vol. 49 (August 2023) , art. 101350  

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