Rational first integrals of the Liénard equations: The solution to the Poincaré problem for the Liénard equations

Autor(es)

Llibre, Jaume ^[1] ; Pessoa, Claudio ^[2] ; Ribeiro, Jarne D. ^[3]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Anais da Academia Brasileira de Ciências; v. 93, n. 4 2021.
• Citações Web of Science: 0

Resumo

Abstract 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 x ¨ + f ( x ) x ˙ + 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. (AU)

• Processo FAPESP: 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 18/19726-5 - Problema de Dulac e do Centro-Foco em Variedades Bidimensionais
• Beneficiário: Cláudio Gomes Pessoa
• Modalidade de apoio: Bolsas no Exterior - Pesquisa