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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Llibre, Jaume [1] ; Pessoa, Claudio [2] ; Ribeiro, Jarne D. [3]
Total Authors: 3
Affiliation:
[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
Total Affiliations: 3
Document type: Journal article
Source: Anais da Academia Brasileira de Ciências; v. 93, n. 4 2021.
Web of Science Citations: 0
Abstract

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)

FAPESP's process: 19/10269-3 - Ergodic and qualitative theories of dynamical systems II
Grantee:Claudio Aguinaldo Buzzi
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 18/19726-5 - Dulac's Problem and of the Focus Center on Two-Dimensional Manifolds
Grantee:Cláudio Gomes Pessoa
Support Opportunities: Scholarships abroad - Research