On the configurations of the singular points and their topological indices for the spatial quadratic polynomial differential systems
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática (Portugal))

Date:	2020
Abstract:	Using the Euler-Jacobi formula there is a 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 polynomial differential systems x˙=P(x,y,z), y˙=Q(x,y,z), z˙=R(x,y,z) with degrees of P, Q and R equal to two when these systems have the maximum number of isolated singular points, i. e. , 8 singular points. In other words we extend the well-known Berlinskii's Theorem for quadratic polynomial differential systems in the plane to the space.
Grants:	Ministerio de Economía y Competitividad MTM2016-77278-P European Commission 777911 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Euler-Jacobi formula ; Singular points ; Topological index ; Polynomial differential systems ; Berlinskii's Theorem
Published in:	Journal of differential equations, Vol. 269, Issue 12 (December 2020) , p. 10571-10586, ISSN 1090-2732

DOI: 10.1016/j.jde.2020.07.022

Postprint 20 p, 782.2 KB

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