On planar polynomial vector fields with elementary first integrals

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Title:	On planar polynomial vector fields with elementary first integrals
Author:	Christopher, Colin; Llibre, Jaume; Pantazi, Chara; Walcher, Sebastian
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.
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Document type:	Article
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Uri:	https://ddd.uab.cat/record/221294