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

Bravo, José Luis a0f02556-de8b-4f92-96b5-220513dc3d86 500 Fernández, Manuel 99cca5ad-f4df-4b98-967c-dd20d5c0d6e1 500 Ojeda, Ignacio 9a8dbcd9-f896-42be-8673-9896f2959caf 500 Sánchez, Fernándo cafce770-2b88-497e-9004-6d3dc540bc6e 500 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 THUMBNAIL Uniqueness-of-limit-cycles.pdf.jpg Uniqueness-of-limit-cycles.pdf.jpg IM Thumbnail image/jpeg 1240 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b3IgaW5jdW1wbGltaWVudG8gZGUgY3VhbHF1aWVyYSBkZSBsYXMgb2JsaWdhY2lvbmVzIGRlcml2YWRhcyBkZWwgQWN1ZXJkbywgcG9yIHZvbHVudGFkIGV4cHJlc2EgZGVsIEF1dG9yCkVuICBwcnVlYmEgZGUgY29uZm9ybWlkYWQsIGxhcyBwYXJ0ZXMgYWNlcHRhbiBlbCBwcmVzZW50ZSBBY3VlcmRvCgoKCgo=