On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves

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Title:	On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves
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:	We give an upper bound for the maximum number N of algebraic limit cycles that a planar polynomial vector field of degree n can exhibit if the vector field has exactly k nonsingular irreducible invariant algebraic curves. Additionally we provide sufficient conditions in order that all the algebraic limit cycles are hyperbolic. We also provide lower bounds for N.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions diferencials ordinàries -Limit cycles -Polynomials -Vector fields -Polinomis -Camps vectorials -Cicles límits -Classificació AMS::34 Ordinary differential equations::34C Qualitative theory -Classificació AMS::34 Ordinary differential equations::34A General theory
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Document type:	Article - Published version Article
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