Some Remarks on the ω-Limit Sets for Plane, Sphere and Projective Plane Analytic Flows

• José Ginés Espín Buendía ^[1] ; Víctor Jiménez López ^[1]
  1. [1] Universidad de Murcia

     Universidad de Murcia

     Murcia, España

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 2, 2017, págs. 293-298
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • We show that Lemma 4.6 (and hence Proposition 4.9) in Jiménez López and Llibre (Adv Math 216: 677–710, 2007) has an essential gap. We amend this gap in the particular cases of the sphere, the plane, the projective plane and the projective plane minus one point, thus the main results in Jiménez López and Llibre (Adv Math 216: 677–710, 2007) remain correct. On the other hand, some counterexamples for the sphere minus two points and for the projective plane minus two points are given;

    as a consequence, Theorems 7.1 and 7.2 in Jiménez López and Llibre (Adv Math 216:

    677–710, 2007) are incomplete.