Quartic Rigid Systems in the Plane and in the Poincaré Sphere

• M. J. Álvarez ^[1] ; J. L. Bravo ^[2] ; L. A. Calderón ^[1]
  1. [1] Universitat de les Illes Balears

     Universitat de les Illes Balears

     Palma de Mallorca, España

     
  2. [2] Universidad de Extremadura

     Universidad de Extremadura

     Badajoz, España

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 5, 2024
• Idioma: inglés
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• Resumen

  • We consider the planar family of rigid systems of the form , where P is any polynomial with monomials of degree one and three. This is the simplest non-trivial family of rigid systems with no rotatory parameters. The family can be compactified to the Poincaré sphere such that the vector field along the equator is not identically null . We study the centers, singular points and limit cycles of that family on the plane and on the sphere.