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

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...

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Bibliographic Details
Main Authors: Jaume Llibre, Daniel Peralta-Salas
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2012-06-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
first integral
vector field
integrating factor
normalizer
Online Access:http://dx.doi.org/10.3842/SIGMA.2012.035
Description
Summary: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.
ISSN:1815-0659

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