On planar polynomial vector fields with elementary first integrals
We show that under rather general conditions a polynomial differential system having an elementary first integral already must admit a Darboux first integral, and we explicitly characterize the vector fields in this class. We also investigate some exceptional cases, i.e. equations admitting an eleme...
| Authors: | , , , |
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| Format: | article |
| Publication Date: | 2019 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/331270 |
| Online Access: | https://hdl.handle.net/2117/331270 https://dx.doi.org/10.1016/j.jde.2019.05.007 |
| Access Level: | Open access |
| Keyword: | Differentiable dynamical systems Random dynamical systems Sistemes dinàmics diferenciables Sistemes dinàmics aleatoris Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics |
| Summary: | We show that under rather general conditions a polynomial differential system having an elementary first integral already must admit a Darboux first integral, and we explicitly characterize the vector fields in this class. We also investigate some exceptional cases, i.e. equations admitting an elementary first integral but not a Darboux first integral. In particular we provide a rather detailed discussion of exceptional elementary first integrals built from algebraic functions of prime degree. |
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