The Euler-Jacobi formula and the planar quadratic-quartic polynomial differential systems

Llibre, Jaume; Valls, Claudia

doi:10.1090/proc/15257

The Euler-Jacobi formula and the planar quadratic-quartic polynomial differential systems
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by Jaume Llibre and Claudia Valls PDF

Proc. Amer. Math. Soc. 149 (2021), 135-141 Request permission

Abstract:

The Euler-Jacobi formula provides an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the planar quadratic-quartic polynomial differential systems when these systems have eight finite singular points.

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