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.
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页数：7
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