Homogeneous polynomial vector fields of degree 2 on the 2--dimensional sphere

• Autores: Jaume Llibre , Claudio Pessoa
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 21, Nº 2, 2006, págs. 167-190
• Idioma: inglés
• Títulos paralelos:
  • Campos vectoriales polinómicos homogéneos de grado 2 sobre la esfera de dos dimensiones
• Enlaces
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• Resumen

  • Let X be a homogeneous polynomial vector field of degree 2 on S2 having finitely many invariant circles. Then, we prove that each invariant circle is a great circle of S2, and at most there are two invariant circles. We characterize the global phase portrait of these vector fields. Moreover, we show that if X has at least an invariant circle then it does not have limit cycles.