Darboux integrating factors: Inverse problems
Christopher, Colin (University of Plymouth. Department of Mathematics and Statistics)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Pantazi, Chara (Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I)
Walcher, Sebastian (Lehrstuhl A fur Mathematik (Germany))

Date:	2011
Abstract:	We discuss planar polynomial vector fields with prescribed Darboux integrating factors, in a nondegenerate affine geometric setting. We establish a reduction principle which transfers the problem to polynomial solutions of certain meromorphic linear systems, and show that the space of vector fields with a given integrating factor, modulo a subspace of explicitly known "standard" vector fields, has finite dimension. For several classes of examples we determine this space explicitly.
Grants:	Ministerio de Educación y Ciencia MTM2005-06098-C02-01 Ministerio de Educación y Ciencia MTM2006-00478 Agència de Gestió d'Ajuts Universitaris i de Recerca 2001/SGR-550
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Published in:	Journal of differential equations, Vol. 250 Núm. 1 (2011) , p. 1-25, ISSN 1090-2732

DOI: 10.1016/j.jde.2010.10.013

Postprint 23 p, 715.3 KB

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