On planar polynomial vector fields with elementary first integrals
dc.contributor.author | Christopher, Colin | |
dc.contributor.author | Llibre, J | |
dc.contributor.author | Pantazi, C | |
dc.contributor.author | Walcher, S | |
dc.date.accessioned | 2019-07-20T22:53:40Z | |
dc.date.accessioned | 2019-07-20T22:56:01Z | |
dc.date.available | 2019-07-20T22:53:40Z | |
dc.date.available | 2019-07-20T22:56:01Z | |
dc.date.issued | 2019-10-05 | |
dc.identifier.issn | 0022-0396 | |
dc.identifier.issn | 1090-2732 | |
dc.identifier.uri | http://hdl.handle.net/10026.1/14666 | |
dc.description.abstract |
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. | |
dc.format.extent | 4572-4588 | |
dc.language | en | |
dc.language.iso | en | |
dc.publisher | Elsevier | |
dc.relation.replaces | http://hdl.handle.net/10026.1/14665 | |
dc.relation.replaces | 10026.1/14665 | |
dc.title | On planar polynomial vector fields with elementary first integrals | |
dc.type | journal-article | |
dc.type | Journal Article | |
plymouth.issue | 8 | |
plymouth.volume | 267 | |
plymouth.publication-status | Published | |
plymouth.journal | Journal of Differential Equations | |
dc.identifier.doi | 10.1016/j.jde.2019.05.007 | |
plymouth.organisational-group | /Plymouth | |
plymouth.organisational-group | /Plymouth/Faculty of Science and Engineering | |
plymouth.organisational-group | /Plymouth/Faculty of Science and Engineering/School of Engineering, Computing and Mathematics | |
plymouth.organisational-group | /Plymouth/REF 2021 Researchers by UoA | |
plymouth.organisational-group | /Plymouth/REF 2021 Researchers by UoA/EXTENDED UoA 10 - Mathematical Sciences | |
plymouth.organisational-group | /Plymouth/REF 2021 Researchers by UoA/UoA10 Mathematical Sciences | |
plymouth.organisational-group | /Plymouth/Users by role | |
plymouth.organisational-group | /Plymouth/Users by role/Academics | |
dcterms.dateAccepted | 2019-04-30 | |
dc.rights.embargodate | 2020-5-13 | |
dc.identifier.eissn | 1090-2732 | |
dc.rights.embargoperiod | Not known | |
rioxxterms.versionofrecord | 10.1016/j.jde.2019.05.007 | |
rioxxterms.licenseref.uri | http://www.rioxx.net/licenses/all-rights-reserved | |
rioxxterms.licenseref.startdate | 2019-10-05 | |
rioxxterms.type | Journal Article/Review |