| Full text | |
| Author(s): |
Total Authors: 3
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| 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
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| 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 |