Morphisms and inverse problems for Darboux integrating factors
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
Walcher, Sebastian (RWTH Aachen(Germany), Lehrstuhl A fur Mathematik)

Date:	2013
Abstract:	Polynomial vector fields which admit a prescribed Darboux integrating factor are quite well-understood when the geometry of the underlying curve is nondegenerate. 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.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-859
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Polynomial differential system ; Invariant algebraic curve ; Darboux integrating factor ; Morphism
Published in:	Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 143 Núm. 6 (2013) , p. 1291-1302, ISSN 1473-7124

DOI: 10.1017/S0308210511001430

Postprint 11 p, 532.6 KB

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