Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations
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Poincaré in 1891 asked about the necessary and sufficient conditions in order to characterize when a polynomial differential system in the plane has a rational first integral. Here we solve this question for the class of Liénard differential equations ẍ + f (x)ẋ + x = 0, being f (x) a polynomial of arbitrary degree. As far as we know it is the first time that all rational first integrals of a relevant class of polynomial differential equations of arbitrary degree has been classified.
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Anais da Academia Brasileira de Ciencias, v. 93, n. 4, 2021.
