On vector fields with simply connected trajectories and one invariant line |
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Authors: | Alvaro Bustinduy Luis Giraldo |
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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 |
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Abstract: | We study polynomial vector fields X on which have simply connected trajectories and satisfy , for a constant and a primitive polynomial . We determine X, up to an algebraic change of coordinates. In particular, we obtain that X is complete. |
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Keywords: | primary 32M25 secondary 32L30 32S65 Foliation transverse to a fibration Simply connected trajectories Eigenfunctions of derivations |
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