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.
|Journal||Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)|
|Publication status||Published - 1 Dec 2012|
- First integral
- Integrating factor
- Vector field