On the local analytic integrability at the singular point of a class of Liénard analytic differential systems

Abstract

We consider the Lienard analytic differential systems x = y, y = -cx - f(x)y, with c ∈ ℝ and f: ℝ → ℝ an analytic function. Then for such systems we characterize the existence of local analytic first integrals in a neighborhood of the singular point located at the origin.