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. © 2010 Elsevier Inc.
Original language | English |
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Pages (from-to) | 1-25 |
Journal | Journal of Differential Equations |
Volume | 250 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2011 |
Keywords
- Integrating factor
- Invariant algebraic curve
- Polynomial differential system