The Euler-Jacobi formula and the planar quadratic-quartic polynomial differential systems
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- by Jaume Llibre and Claudia Valls
- Proc. Amer. Math. Soc. 149 (2021), 135-141
- 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.References
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Bibliographic Information
- Jaume Llibre
- Affiliation: Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
- MR Author ID: 115015
- ORCID: 0000-0002-9511-5999
- Email: jllibre@mat.uab.cat
- Claudia Valls
- Affiliation: Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais 1049–001, Lisboa, Portugal
- MR Author ID: 636500
- Email: cvalls@math.ist.utl.pt
- 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
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 135-141
- MSC (2010): Primary 34A05; Secondary 34C05, 37C10
- DOI: https://doi.org/10.1090/proc/15257
- MathSciNet review: 4172592