Inverse problems for multiple invariant curves

Colin Christopher, Jaume Llibre, Chara Pantazi, Sebastian Walcher

Research output: Contribution to journalArticleResearchpeer-review

14 Citations (Scopus)


Planar polynomial vector fields which admit invariant algebraic curves, Darboux integrating factors or Darboux first integrals axe of special interest. We solve the inverse problem for invariant algebraic curves with a given multiplicity and for integrating factors, under generic assumptions regarding the (multiple) invariant algebraic curves involved. In particular, we prove, in this generic scenario, that the existence of a Darboux integrating factor implies Darboux integrability. Furthermore, we construct examples in which the genericity assumption does not hold and indicate that the situation is different for these. © 2007 The Royal Society of Edinburgh.
Original languageEnglish
Pages (from-to)1197-1226
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Issue number6
Publication statusPublished - 14 Dec 2007


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