New Family of Centers of Planar Polynomial Differential Systems of Arbitrary Even Degree

  • Jaume LlibreEmail author
  • Marzieh Mousavi
  • Arefeh Nabavi


The problem of distinguishing between a focus and a center is one of the classical problems in the qualitative theory of planar differential systems. In this paper, we provide a new family of centers of polynomial differential systems of arbitrary even degree. Moreover, we classify the global phase portraits in the Poincaré disc of the centers of this family having degree 2, 4, and 6.


Poincaré compactification Center First integral Invariant algebraic curve 

Mathematics Subject Classification (2010)

Primary 34A05 Secondary 34C05 37C10 


Funding Information

This work is supported by the Ministerio de Economìa, Industria y competitividad, Agencia Estatal de Investigación grant MTM2016-77278-P (FEDER), the Agència de Gestió d’Ajusts Universitaris i de Recerca grant 2017SGR1617, and the European project Dynamics-H2020-MSCA-RISE-2017-777911.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBarcelonaSpain
  2. 2.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran

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