Rational first integrals of the Lienard equations: The solution to the Poincare problem for the Lienard equations

被引：1

作者：

Llibre, Jaume ^{[1
]}

Pessoa, Claudio ^{[2
]}

Ribeiro, Jarne D. ^{[3
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia, Spain

[2] Univ Estadual Paulista, Dept Matemat, IBILCE, Campus Sao Jose do Rio Preto, BR-15054000 Sao Jose Do Rio Preto, SP, Brazil

[3] IFSULDEMINAS, Inst Fed Educ Ciencia & Tecnol Sul Minas Gerais, Rua Mario Ribola 409,Penha 2, BR-37903358 Passos, MG, Brazil

来源：

ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS | 2021年 / 93卷 / 04期

基金：

巴西圣保罗研究基金会; 欧盟地平线“2020”;

关键词：

Lienard equation; rational first integral; Poincare problem; polinomial differential equation; LIMIT-CYCLES;

D O I：

10.1590/0001-3765202120191139

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

Poincare 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 Lienard differential equations (sic) + f (x)(x)over dot + 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.

引用

页数：7

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