Linearizability and integrability of vector fields via commutation |
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Authors: | Jaume Giné Maite Grau |
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Institution: | Departamento de Matemàtica, Universitat de Lleida, Avda. Jaume II, 69, 25001 Lleida, Spain |
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Abstract: | In this paper, we consider complex smooth and analytic vector fields X in a neighborhood of a nondegenerate singular point. It is proved the equivalence between linearizability and commutation, i.e., the existence of a commuting vector field Y such that the Lie brackets X,Y]≡0. For complex smooth and analytic vector fields in the plane and in a neighborhood of a nondegenerate singular point, it is also proved the equivalence between integrability and the existence of a smooth vector field Y, such that Y is a normalizer of X, i.e., X,Y]=μX. |
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Keywords: | Polynomial vector fields Linearizability Integrability Commutation |
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