A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2012
• Main Authors: Llibre, J., Peralta-Salas, D.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2012
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148427
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers / J. Llibre, D. Peralta-Salas // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ.

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...