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dc.contributor.authorChristopher, Colin
dc.contributor.authorLlibre, J
dc.contributor.authorPantazi, C
dc.contributor.authorWalcher, S
dc.date.accessioned2019-07-20T22:53:40Z
dc.date.accessioned2019-07-20T22:56:01Z
dc.date.available2019-07-20T22:53:40Z
dc.date.available2019-07-20T22:56:01Z
dc.date.issued2019-10-05
dc.identifier.issn0022-0396
dc.identifier.issn1090-2732
dc.identifier.urihttp://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.extent4572-4588
dc.languageen
dc.language.isoen
dc.publisherElsevier
dc.relation.replaceshttp://hdl.handle.net/10026.1/14665
dc.relation.replaces10026.1/14665
dc.titleOn planar polynomial vector fields with elementary first integrals
dc.typejournal-article
dc.typeJournal Article
plymouth.issue8
plymouth.volume267
plymouth.publication-statusPublished
plymouth.journalJournal of Differential Equations
dc.identifier.doi10.1016/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.dateAccepted2019-04-30
dc.rights.embargodate2020-5-13
dc.identifier.eissn1090-2732
dc.rights.embargoperiodNot known
rioxxterms.versionofrecord10.1016/j.jde.2019.05.007
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.licenseref.startdate2019-10-05
rioxxterms.typeJournal Article/Review


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