On the 16th Hilbert problem for algebraic limit cycles

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/8746

dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.contributor	Universitat Politècnica de Catalunya. MMAC - Models Matemàtics aplicats a les ciencies humanes i de la natura
dc.contributor.author	Llibre Saló, Jaume
dc.contributor.author	Ramírez Inostroza, Rafael Orlando
dc.contributor.author	Sadovskaia Nurimanova, Natalia Guennadievna
dc.date	2010-03-15
dc.identifier.citation	Llibre, J.; Ramírez, R.; Sadovskaia, N. On the 16th Hilbert problem for algebraic limit cycles. "Journal of differential equations", 15 Març 2010, vol. 248, núm. 6, p. 1401-1409.
dc.identifier.citation	0022-0396
dc.identifier.citation	10.1016/j.jde.2009.11.023
dc.identifier.uri	http://hdl.handle.net/2117/8746
dc.language.iso	eng
dc.relation	http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WJ2-4XVBB73-1-1&_cdi=6866&_user=1517299&_pii=S0022039609004458&_origin=search&_coverDate=03%2F15%2F2010&_sk=997519993&view=c&wchp=dGLbVlz-zSkWA&md5=8166c6c31227d48dc5dec5dc33220d81&ie=/sdarticle.pdf
dc.rights	Attribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis
dc.subject	Limit cycles
dc.subject	Polynomials
dc.subject	Mathematics--Problems, exercises, etc.
dc.subject	Algebra
dc.subject	Polinomis
dc.subject	Matemàtica -- Problemes, exercicis, etc.
dc.subject	Àlgebra
dc.title	On the 16th Hilbert problem for algebraic limit cycles
dc.type	info:eu-repo/semantics/publishedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	For a polynomial planar vector field of degree n ≥ 2 with generic invariant algebraic curves we show that the maximum number of algebraic limit cycles is 1 + (n − 1)(n − 2)/2 when n is even, and (n − 1)(n − 2)/2 when n is odd. Furthermore, these upper bounds are reached.

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