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On the 16th Hilbert problem for limit cycles on nonsingular algebraic curves |
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| Authors: | Jaume Llibre Rafael Ramírez Natalia Sadovskaia |
| Institution: | 1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain;2. Departament d''Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Avinguda dels Països Catalans 26, 43007 Tarragona, Catalonia, Spain;3. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, C. Pau Gargallo 5, 08028 Barcelona, Catalonia, Spain |
| 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. |
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