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| Pàgina inicial > Articles > Articles publicats > Analytic integrability of a class of planar polynomial differential systems |
(Universitat Autònoma de Barcelona. Departament de Matemàtiques) (Universidade Técnica de Lisboa. Departamento de Matemática)| Data: | 2015 |
| Resum: | In this paper we find necessary and sufficient conditions in order that the differential systems of the form ˙x = xf(y), ˙y = g(y), with f and g polynomials, have a first integral which is analytic in the variable x and meromorphic in the variable y. We also characterize their analytic first integrals in both variables x and y. These polynomial differential systems are important because after a convenient change of variables they contain all quasi-homogeneous polynomial differential systems in R2. |
| Ajuts: | Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 318999 European Commission 316338 |
| Nota: | Agraïments: The second author was supported by Portuguese National Funds through FCT - Fundacâo para a Ciência e a Tecnologia within the project PTDC/MAT/117106/2010 and by CAMGSD. |
| Drets: | Tots els drets reservats.  |
| Llengua: | Anglès |
| Document: | Article ; recerca ; Versió acceptada per publicar |
| Matèria: | Planar polynomial systems ; Quasi-homogeneous polynomial differential systems ; Analytic first integrals ; Pseudo-meromorphic first integrals |
| Publicat a: | Discrete and continuous dynamical systems. Series B, Vol. 20 Núm. 8 (2015) , p. 2657-2661, ISSN 1553-524X |
6 p, 641.7 KB |
