Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations

Llibre, Jaume; Pessoa, Claudio [UNESP]; Ribeiro, Jarne D.

Rational first integrals of the liénard equations: The solution to the poincaré problem for the liénard equations

Data

2021-01-01

Autores

Llibre, Jaume

Pessoa, Claudio

Ribeiro, Jarne D.

Tipo

Artigo

Resumo

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.