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A note on the first integrals of vector fields with integrating factors and normalizers
Symmetry, integrability and geometry: methods and applications, Tome 8 (2012) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: first integral, vector field, integrating factor, normalizer. 
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     author = {Jaume Llibre and Daniel Peralta-Salas},
     title = {A note on the first integrals of vector fields with integrating factors and normalizers},
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     year = {2012},
     volume = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a34/}
}
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Jaume Llibre; Daniel Peralta-Salas. A note on the first integrals of vector fields with integrating factors and normalizers. Symmetry, integrability and geometry: methods and applications, Tome 8 (2012). http://geodesic.mathdoc.fr/item/SIGMA_2012_8_a34/

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