On the nonexistence of Liouvillian first integrals for generalized Liénard polynomial differential systems

Guillaume Chèze (1) , Thomas Cluzeau (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 XLIM-DMI - DMI

We consider generalized Liénard polynomial differential systems. In their work, Llibre and Valls have shown that, except in some particular cases, such systems have no Liouvillian first integral. In this letter, we give a direct and shorter proof of this result.

Mots clés: Polynomial vector fields; first integrals; invariant algebraic curves; Liénard polynomial differential systems

Domaines: Analyse classique [math.CA]; Systèmes Solubles et Intégrables [nlin.SI]

Guillaume Chèze, Thomas Cluzeau. On the nonexistence of Liouvillian first integrals for generalized Liénard polynomial differential systems. Journal of Nonlinear Mathematical Physics, 2013, 20 (4), pp.475-479. ⟨10.1080/14029251.2013.868260⟩. ⟨hal-00864791⟩