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

Symmetry Integrability and Geometry-Methods and Applications

article

Jaume Llibre¹  Daniel Peralta-Salas² 

[1] Departament de Matemàtiques, Universitat Autònoma de Barcelona;Instituto de Ciencias Matemáticas

关键词: first integral;    vector field;    integrating factor;    normalizer;   

DOI  :  10.3842/SIGMA.2012.035

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown