The generalized Liénard polynomial differential systems x'=y,y'= -g(x) - f (x)y with deg g = deg f 1 are not Liouvillian integrable
We prove the nonexistence of Liouvillian first integrals for the generalized Li\'enard polynomial differential systems of the form x' = y, y'=-g(x)-f(x)y, where g(x) and f(x) are arbitrary polynomials such that g = f 1.
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2015 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglês |
| OAI Identifier: | oai:ddd.uab.cat:145352 |
| Acesso em linha: | https://ddd.uab.cat/record/145352 https://dx.doi.org/urn:doi:10.1016/j.bulsci.2014.08.010 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Darboux polynomial Exponential factor Liénard polynomial differential system Liouvillian first integrals |
| Resumo: | We prove the nonexistence of Liouvillian first integrals for the generalized Li\'enard polynomial differential systems of the form x' = y, y'=-g(x)-f(x)y, where g(x) and f(x) are arbitrary polynomials such that g = f 1. |
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