On planar polynomial vector fields with elementary first integrals

Colin Christopher, Jaume Llibre, Chara Pantazi, Sebastian Walcher

Research output: Contribution to journalArticleResearch

6 Citations (Scopus)


© 2019 Elsevier Inc. 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.
Original languageEnglish
Pages (from-to)4572-4588
JournalJournal of Differential Equations
Publication statusPublished - 5 Oct 2019


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