On vector fields with simply connected trajectories and one invariant line期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On vector fields with simply connected trajectories and one invariant line

Authors:	Alvaro Bustinduy Luis Giraldo

Affiliation:	1. Departamento de Ingeniería Industrial, Escuela Politécnica Superior, Universidad Antonio de Nebrija, Calle Pirineos 55, 28040 Madrid, Spain;2. Instituto de Matemática Interdisciplinar (IMI), Departamento de Geometría y Topología, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain

Abstract:	We study polynomial vector fields X on $C^{2}$ which have simply connected trajectories and satisfy $d P (X) = a ? P$ , for a constant $a \in C^{?}$ and a primitive polynomial $P \in C [x, y]$ . We determine X, up to an algebraic change of coordinates. In particular, we obtain that X is complete.

Keywords:	primary 32M25 secondary 32L30 32S65 Foliation transverse to a fibration Simply connected trajectories Eigenfunctions of derivations
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