Planar polynomial vector fields having a polynomial first integral can be obtained from linear systems

Belen García , Héctor Giacomini (1) , Jesús S. Pérez del Río

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

We consider in this work planar polynomial differential systems having a polynomial first integral. We prove that these systems can be obtained from a linear system through a polynomial transformation of variables.

Mots clés: polynomial differential system; first integral

Domaines: Systèmes dynamiques [math.DS]

Belen García, Héctor Giacomini, Jesús S. Pérez del Río. Planar polynomial vector fields having a polynomial first integral can be obtained from linear systems. Applied Mathematics Letters, 2011, 24 (7), pp.1115-1119. ⟨10.1016/j.aml.2011.01.036⟩. ⟨hal-01171036⟩