Counterexample to a conjecture on the algebraic limit cycles of polynomial vector fields
| Autor: | Llibre Saló, Jaume, Pantazi, Chara|||0000-0002-4394-404X |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2004 |
| Předmět: |
Geometry
Algebraic Differential equations Geometria algebraica polynomial vector fields 34 Ordinary differential equations::34C Qualitative theory [Classificació AMS] 14 Algebraic geometry::14P Real algebraic and real analytic geometry [Classificació AMS] Geometria analítica Equacions diferencials ordinàries algebraic limit cycles |
| Zdroj: | UPCommons. Portal del coneixement obert de la UPC Universitat Politècnica de Catalunya (UPC) |
| Popis: | In Geometriae Dedicata 79 (2000), 101{108, Rudolf Winkel conjectured: For a given algebraic curve f = 0 of degree m > 4 there is in general no polynomial vector ¯eld of degree less than 2m ¡ 1 leaving invariant f = 0 and having exactly the ovals of f = 0 as limit cycles. Here we show that this conjecture is not true. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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