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Global phase portraits for the Abel quadratic polynomial differential equations of second kind with $Z_2$-symmetries

  • Jaume Llibre,
    Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
  • Claudia Valls,
    Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais 1049--001, Lisboa, Portugal
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Abstract

We provide normal forms and the global phase portraits on the Poincaré disk for all Abel quadratic polynomial differential equations of the second kind with $\mathbb Z_2$-symmetries.
Keywords: Abel polynomial differential system of the second kind, vector field, phase portrait Abel polynomial differential system of the second kind, vector field, phase portrait
MSC Classifications: 37J35, 37K10 show english descriptions Completely integrable systems, topological structure of phase space, integration methods
Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
37J35 - Completely integrable systems, topological structure of phase space, integration methods
37K10 - Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies (KdV, KP, Toda, etc.)
 

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