Polynomial and rational first integrals for planar quasi-homogeneous polynomial differential sytems
In this paper we find necessary and sufficient conditions in order that a planar quasi-homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi-homogeneous polynomial differential system can be transformed into a differential syste...
| Autores: | , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2013 |
| País: | España |
| Recursos: | Universitat Autònoma de Barcelona |
| Repositório: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglês |
| OAI Identifier: | oai:ddd.uab.cat:150596 |
| Acesso em linha: | https://ddd.uab.cat/record/150596 https://dx.doi.org/urn:doi:10.3934/dcds.2013.33.4531 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Quasi-homogeneous polynomial differential equations Integrability problem Polynomial first integral Rational first integral |
| Resumo: | In this paper we find necessary and sufficient conditions in order that a planar quasi-homogeneous polynomial differential system has a polynomial or a rational first integral. We also prove that any planar quasi-homogeneous polynomial differential system can be transformed into a differential system of the form u˙ = uf(v), ˙v = g(v) with f(v) and g(v) polynomials, and vice versa. |
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