Centers: their integrability and relations with the divergence

• J. Llibre ^[1]
  1. [1] Universitat Autònoma de Barcelona

     Universitat Autònoma de Barcelona

     Barcelona, España

     
• Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 1, Nº. 1, 2016, págs. 74-81
• Idioma: inglés
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• Resumen

  • This is a brief survey on the centers of the analytic differential systems in R 2 . First we consider the kind of integrability of the different types of centers, and after we analyze the focus–center problem, i.e. how to distinguish a center from a focus. This is a difficult problem which is not completely solved. We shall present some recent results using the divergence of the differential system.