On the 16th Hilbert problem for algebraic limit cycles

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Title:	On the 16th Hilbert problem for algebraic limit cycles
Author:	Llibre Saló, Jaume; Ramírez Inostroza, Rafael Orlando; Sadovskaia Nurimanova, Natalia Guennadievna
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. MMAC - Models Matemàtics aplicats a les ciencies humanes i de la natura
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.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de cossos i polinomis -Limit cycles -Polynomials -Mathematics--Problems, exercises, etc. -Algebra -Polinomis -Matemàtica -- Problemes, exercicis, etc. -Àlgebra
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Published version Article
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