Topological classification of limit periodic sets of polynomial planar vector fields

• Autores: Andre Belotto da Silva, José Ginés Espín Buendía
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 63, Nº 1, 2019, págs. 105-123
• Idioma: inglés
• DOI: 10.5565/PUBLMAT6311903
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• Resumen

  • 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.