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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: 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