Psi-series of quadratic vector fields on the plane

• Autores: Amadeu Delshams i Valdés, Arnau Mir Torres
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 41, Nº 1, 1997 (Ejemplar dedicado a: Proceedings of the Symposium on Planar Vector Fields), págs. 101-125
• Idioma: inglés
• Títulos paralelos:
  • Series psi de campos vectoriales cuadráticos en el plano
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• Resumen

  • Psi-series (i.e., logarithmic series) for the solutions of quadratic vector fields on the plane are considered. Its existence and convergence is studied, and an algorithm for the location of logarithmic singularities is developed. Moreover, the relationship between psi-series and non-integrability is stressed and in particular it is proved that quadratic systems with psi-series that are not Laurent series do not have an algebraic first integral. Besides, a criterion about non-existence of an analytic first integral is given.