The solution of the Poincaré problem on the rational first integral for the Liénard polynomial differential equations
In this work we classify the polynomial Liénard differential equations ̈𝑥 + 𝑓(𝑥) ̇𝑥 + 𝑥 = 0, having a rational first integral. Such classification was asked by Poincaré in 1891 for any general polynomial differential systems in the plane R2 . As far as we know it is the first time that the complete classification is given for a relevant class of polynomial differential equations of arbitrary degree.
Journal or Serie
Chaos, Solitons & Fractals, 2023, vol. 167, 113013