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

  1. José Ginés Espín Buendía 1
  2. Víctor Jiménez López 1
  1. 1 Universidad de Murcia
    info

    Universidad de Murcia

    Murcia, España

    ROR https://ror.org/03p3aeb86

Revista:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Año de publicación: 2017

Volumen: 16

Número: 2

Páginas: 293-298

Tipo: Artículo

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Otras publicaciones en: Qualitative theory of dynamical systems

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.

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Información de financiación

This work has been partially supported by Ministerio de Econom?a y Competitividad, Spain, grants MTM2011-23221 y MTM2014-52920-P, and Fundaci?n S?neca (Comunidad Aut?noma de la Regi?n de Murcia, Spain), grant 19294/PI/14. The first author is also supported by Fundaci?n S?neca by means of the program ?Contratos Predoctorales de Formaci?n del Personal Investigador?, grant 18910/FPI/13.

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