The 16th Hilbert problem restricted to circular algebraic limit cycles
| Autor: | Rafael Ramírez, Jaume Llibre, Natalia Sadovskaia, Valentín Ramírez |
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| Rok vydání: | 2016 |
| Předmět: |
Planar polynomial differential system
Applied Mathematics 010102 general mathematics Darboux integrability Invariant algebraic circles Polarization of an algebraic form Algebraic extension Dimension of an algebraic variety 01 natural sciences Algebraic element 010101 applied mathematics Combinatorics Algebraic cycle Algebraic function Geometric invariant theory 0101 mathematics Hilbert's sixteenth problem Polynomial vector fields Analysis Mathematics |
| Zdroj: | Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona Recercat. Dipósit de la Recerca de Catalunya instname Recercat: Dipósit de la Recerca de Catalunya Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Popis: | Agraïments: FEDER-UNAB10-4E-378 and Consolider CSD2007-00004 "ES" We prove the following two results. First every planar polynomial vector field of degree S with S invariant circles is Darboux integrable without limit cycles. Second a planar polynomial vector field of degree S admits at most S - 1 invariant circles which are algebraic limit cycles. In particular we solve the 16th Hilbert problem restricted to algebraic limit cycles given by circles, because a planar polynomial vector field of degree S has at most S - 1 algebraic limit cycles given by circles, and this number is reached. |
| Databáze: | OpenAIRE |
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