Some Remarks on the ω-Limit Sets for Plane, Sphere and Projective Plane Analytic Flows
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Universidad de Murcia
info
ISSN: 1575-5460
Datum der Publikation: 2017
Ausgabe: 16
Nummer: 2
Seiten: 293-298
Art: Artikel
Andere Publikationen in: Qualitative theory of dynamical systems
Zusammenfassung
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.
Informationen zur Finanzierung
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.Geldgeber
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- 19294/PI/14
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Ministerio de Economía y Competitividad
Spain
- MTM2011-23221 y MTM2014-52920-P