Analytic integrability of a class of planar polynomial differential systems
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 integra...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2015 |
| Country: | España |
| Institution: | Universitat Autònoma de Barcelona |
| Repository: | Dipòsit Digital de Documents de la UAB |
| Language: | English |
| OAI Identifier: | oai:ddd.uab.cat:169430 |
| Online Access: | https://ddd.uab.cat/record/169430 https://dx.doi.org/urn:doi:10.3934/dcdsb.2015.20.2657 |
| Access Level: | Open access |
| Keyword: | Planar polynomial systems Quasi-homogeneous polynomial differential systems Analytic first integrals Pseudo-meromorphic first integrals |
| Summary: | 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. |
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