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Darboux integrating factors: Inverse problems |
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| Authors: | Colin Christopher Sebastian Walcher |
| Institution: | a Department of Mathematics and Statistics, University of Plymouth, Plymouth PL2 3AJ, UK b Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain c Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, EPSEB, Av. Doctor Marañón, 44-50, 08028 Barcelona, Spain d Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen, Germany |
| 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. |
| Keywords: | 34C05 34A34 34C14 |
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