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23 p, 715.3 KB 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))
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. [...]
2011 - 10.1016/j.jde.2010.10.013
Journal of differential equations, Vol. 250 Núm. 1 (2011) , p. 1-25  
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