Morphisms and inverse problems for Darboux integrating factors

Jaume Llibre, Chara Pantazi, Sebastian Walcher

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)


Polynomial vector fields which admit a prescribed Darboux integrating factor are quite well understood when the geometry of the underlying curve is non-degenerate. In the general setting, morphisms of the affine plane may remove degeneracies of the curve, and thus allow more structural insight. In the present paper we establish some properties of integrating factors subjected to morphisms, and we discuss in detail one particular class of morphisms related to finite reflection groups. The results indicate that degeneracies for the underlying curve generally impose additional restrictions on vector fields admitting a given integrating factor. © Royal Society of Edinburgh 2013.
Original languageEnglish
Pages (from-to)1291-1302
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Issue number6
Publication statusPublished - 1 Jan 2013


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