The Euler-Jacobi formula and the planar quadratic-quartic polynomial differential systems
Authors:
Jaume Llibre and Claudia Valls
Journal:
Proc. Amer. Math. Soc. 149 (2021), 135-141
MSC (2010):
Primary 34A05; Secondary 34C05, 37C10
DOI:
https://doi.org/10.1090/proc/15257
Published electronically:
October 16, 2020
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Abstract | References | Similar Articles | Additional Information
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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Additional Information
Jaume Llibre
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
Email:
jllibre@mat.uab.cat
Claudia Valls
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1049–001, Lisboa, Portugal
Email:
cvalls@math.ist.utl.pt
DOI:
https://doi.org/10.1090/proc/15257
Keywords:
Euler-Jacobi formula,
singular points,
topological index,
polynomial differential systems
Received by editor(s):
March 21, 2019
Received by editor(s) in revised form:
June 10, 2019
Published electronically:
October 16, 2020
Additional Notes:
The first author was supported by the Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación grant MTM2016-77278-P (FEDER), the Agència de Gestió d’Ajuts Universitaris i de Recerca grant 2017SGR1617, and the H2020 European Research Council grant MSCA-RISE-2017-777911.
The second author was partially supported by FCT/Portugal through UID/MAT/04459/2013.
Communicated by:
Wenxian Shen
Article copyright:
© Copyright 2020
American Mathematical Society
