Classification of Global Phase Portrait of Planar Quintic Quasi-Homogeneous Coprime Polynomial Systems

• BaoHua Qiu ^[1] ; HaiHua Liang ^[1]
  1. [1] Guangdong Polytechnic Normal University

     Guangdong Polytechnic Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 2, 2017, págs. 417-451
• Idioma: inglés
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• Resumen

  • This paper is devoted to the complete classification of global phase portraits (short for GPP) of quasi-homogeneous but non-homogeneous coprime planar quintic polynomial differential systems (short for QCQS). We firstly study the canonical forms of QCQS. It is shown that these canonical forms can have 0, 1, 2, 4 parameters.

    Then, we investigate the global topological structures of all canonical forms, by using the quasi-homogeneous blow-up technique for the finite singularities and the Poincaré–Lyapunov compactification for the infinite singularities. We finally perform a topological classification for the set of GPP.