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oai:uvadoc.uva.es:10324/407272021-06-24T07:41:23Zcom_10324_32197com_10324_952com_10324_894col_10324_32199

Uniqueness of limit cycles for quadratic vector fields Bravo, José Luis Fernández, Manuel Ojeda, Ignacio Sánchez, Fernándo 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. 2020-04-06T19:33:18Z 2020-04-06T19:33:18Z 2020-04-06T19:33:18Z 2019 info:eu-repo/semantics/article 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 eng http://www.aimsciences.org/article/doi/10.3934/dcds.2019020 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 American Institute of Mathematical Sciences