Generalized analytic integrability of a class of polynomial differential systems in C2
This paper study the type of integrability of differential systems with separable variables x˙=h(x)f(y), y˙ = g(y), where h, f and g are polynomials. We provide a criterion for the existence of generalized analytic first integrals of such differential systems. Moreover we characterize the polynomial...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:257125 |
| Acceso en línea: | https://ddd.uab.cat/record/257125 https://dx.doi.org/urn:doi:10.1007/s10440-021-00407-4 |
| Access Level: | acceso abierto |
| Palabra clave: | Polynomial systems Generalized analytic integrability Polynomial first integrals Residue |
| Sumario: | This paper study the type of integrability of differential systems with separable variables x˙=h(x)f(y), y˙ = g(y), where h, f and g are polynomials. We provide a criterion for the existence of generalized analytic first integrals of such differential systems. Moreover we characterize the polynomial integrability of all such systems. In the particular case h(x) = (ax+ b) we provide necessary and sufficient conditions in order that this subclass of systems has a generalized analytic first integral. These results extend known results from Giné et al. (Discrete Contin. Dyn. Syst. 33:4531-4547, 2013) and Llibre and Valls (Discrete Contin. Dyn. Syst., Ser. B 20:2657-2661, 2015). Such differential systems of separable variables are important due to the fact that after a blow-up change of variables any planar quasi-homogeneous polynomial differential system can be transformed into a special differential system of separable variables x˙ = xf(y), y˙ = g(y), with f and g polynomials. |
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