The Classical and Improved Euler-Jacobi Formula and Polynomial Vector Fields in Rn
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)

Date:	2024
Abstract:	The classical and the new Euler-Jacobi formulae for simple and double points provide an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using these formulae we obtain the geometrical configuration of the singular points together with their topological indices for several classes of polynomial differential systems in R when these differential systems, having the maximum number of singular points, either all their singular points are simple, or at most one singular point is double (i. e. it has multiplicity two).
Grants:	European Commission 777911 Agencia Estatal de Investigación MTM2016-77278-P Agencia Estatal de Investigación PID2019-104658GB-I00
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Euler-Jacobi formula ; Singular points ; Topological index ; Polynomial differential systems
Published in:	Journal of dynamics and differential equations, Vol. 36,issue 3 (September 2024) , p. 2093-2110, ISSN 1572-9222

DOI: 10.1007/s10884-022-10191-w

Postprint 19 p, 329.0 KB

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