Topological classification of limit periodic sets of polynomial planar vector fields

  1. da Silva, Andre Belotto
  2. Espín Buendía, José Ginés
Zeitschrift:
Publicacions matematiques

ISSN: 0214-1493

Datum der Publikation: 2019

Ausgabe: 63

Nummer: 1

Seiten: 105-123

Art: Artikel

DOI: 10.5565/PUBLMAT6311903 DIALNET GOOGLE SCHOLAR lock_openDDD editor

Andere Publikationen in: Publicacions matematiques

Zusammenfassung

We characterize the limit periodic sets of families of algebraic planar vector fields up to homeomorphisms. We show that any limit periodic set is topologically equivalent to a compact and connected semialgebraic set of the sphere of dimension 0 or 1. Conversely, we show that any compact and connected semialgebraic set of the sphere of dimension 0 or 1 can be realized as a limit periodic set.

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Acknowledgements. We would like to thank the anonymous referee for the useful comments and the University of Toronto for its hospitality. The work of the first author is supported by LabEx CIMI. The second author is supported by Fundación Séneca through the program “Contra-tos Predoctorales de Formación del Personal Investigador”, grant 18910/ FPI/13 and by the MINECO grants MTM2014-52920-P.

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