TY - JOUR

T1 - Morphisms and inverse problems for Darboux integrating factors

AU - Llibre, Jaume

AU - Pantazi, Chara

AU - Walcher, Sebastian

PY - 2013/1/1

Y1 - 2013/1/1

N2 - Polynomial vector fields which admit a prescribed Darboux integrating factor are quite well understood when the geometry of the underlying curve is non-degenerate. In the general setting, morphisms of the affine plane may remove degeneracies of the curve, and thus allow more structural insight. In the present paper we establish some properties of integrating factors subjected to morphisms, and we discuss in detail one particular class of morphisms related to finite reflection groups. The results indicate that degeneracies for the underlying curve generally impose additional restrictions on vector fields admitting a given integrating factor. © Royal Society of Edinburgh 2013.

AB - Polynomial vector fields which admit a prescribed Darboux integrating factor are quite well understood when the geometry of the underlying curve is non-degenerate. In the general setting, morphisms of the affine plane may remove degeneracies of the curve, and thus allow more structural insight. In the present paper we establish some properties of integrating factors subjected to morphisms, and we discuss in detail one particular class of morphisms related to finite reflection groups. The results indicate that degeneracies for the underlying curve generally impose additional restrictions on vector fields admitting a given integrating factor. © Royal Society of Edinburgh 2013.

U2 - https://doi.org/10.1017/S0308210511001430

DO - https://doi.org/10.1017/S0308210511001430

M3 - Article

VL - 143

SP - 1291

EP - 1302

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 6

ER -