TY - JOUR
T1 - Darboux integrating factors: Inverse problems
AU - Christopher, Colin
AU - Llibre, Jaume
AU - Pantazi, Chara
AU - Walcher, Sebastian
PY - 2011/1/1
Y1 - 2011/1/1
N2 - 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.
AB - 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.
KW - Integrating factor
KW - Invariant algebraic curve
KW - Polynomial differential system
UR - https://www.scopus.com/pages/publications/78149283646
U2 - 10.1016/j.jde.2010.10.013
DO - 10.1016/j.jde.2010.10.013
M3 - Article
SN - 0022-0396
VL - 250
SP - 1
EP - 25
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 1
ER -