Polynomial differential equations with many real ovals in the same algebraic complex solution

• Autores: Alcides Lins-Neto
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 55, Nº 2, 2011, págs. 379-399
• Idioma: inglés
• DOI: 10.5565/publmat_55211_06
• Enlaces
  • Texto completo
• Resumen

  • Let FolR(2, d) be the space of real algebraic foliations of degree d in RP(2). For fixed d, let IntR(2, d) = {F 2 FolR(2, d) | F has a non-constant rational first integral}. Given F 2 IntR(2, d), with primitive first integral G, set O(F) = number of real ovals of the generic level (G = c). Let O(d) = sup{O(F) | F 2 IntR(2, d)}.

    The main purpose of this paper is to prove that O(d) = +1 for all d  5.