The solution of the Poincaré problem on the rational first integral for the Liénard polynomial differential equations
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Date
2023
Authors
Giné, Jaume
Llibre, Jaume
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Abstract
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.
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Chaos, Solitons & Fractals, 2023, vol. 167, 113013