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A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
We prove a sufficient condition for the existence of explicit first integrals
for vector fields which admit an integrating factor. This theorem recovers and
extends previous results in the literature on the integrability of vector
fields which are volume preserving and possess nontrivial normalizers. Our
approach is geometric and coordinate-free and hence it works on any smooth
orientable manifold
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