Morphisms and inverse problems for Darboux integrating factors

Jaume Llibre, Chara Pantazi, Sebastian Walcher

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Resum

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.
Idioma originalEnglish
Pàgines (de-a)1291-1302
RevistaProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volum143
Número6
DOIs
Estat de la publicacióPublicada - 1 de gen. 2013

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