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Bravo, José Luis Fernández, Manuel Ojeda, Ignacio Sánchez, Fernándo 2020-04-06T19:33:18Z 2020-04-06T19:33:18Z 2019 Discrete and Continuous Dynamical Systems, 2019, vol. 39, n. 1. p. 483-502 1553-5231 http://uvadoc.uva.es/handle/10324/40727 10.3934/dcds.2019020 Producción Científica This article deals with the study of the number of limit cycles surrounding a critical point of a quadratic planar vector field, which, in normal form, can be written as x ′ = a1x − y − a3x 2 + (2a2 + a5)xy+a6y 2 , y ′ = x+a1y+a2x 2+(2a3+a4)xy−a2y 2 . In particular, we study the semi-varieties defined in terms of the parameters a1, a2, . . . , a6 where some classical criteria for the associated Abel equation apply. The proofs will combine classical ideas with tools from computational algebraic geometry. Agencia Estatal de Investigación - Fondo Europeo de Desarrollo Regional (grant MTM 2011-22751) Junta de Extremadura (grant GR15055) Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (grant MTM2015-65764-C3-1-P) application/pdf eng American Institute of Mathematical Sciences info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by-nc-nd/4.0/ © 2019 American Institute of Mathematical Sciences Attribution-NonCommercial-NoDerivatives 4.0 Internacional Abel equation Ecuación de Abel Closed solution Solución en forma cerrada Periodic solution Solución periódica Limit cycles Ciclos límite Uniqueness of limit cycles for quadratic vector fields info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion http://www.aimsciences.org/article/doi/10.3934/dcds.2019020 SI