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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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

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spelling	doaj-1065ff297e1d42ed98ccb2f063d7a17f2020-11-24T22:27:23ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592012-06-018035A Note on the First Integrals of Vector Fields with Integrating Factors and NormalizersJaume LlibreDaniel Peralta-SalasWe 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. http://dx.doi.org/10.3842/SIGMA.2012.035first integralvector fieldintegrating factornormalizer
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jaume Llibre Daniel Peralta-Salas
spellingShingle	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 first integral vector field integrating factor normalizer
author_facet	Jaume Llibre Daniel Peralta-Salas
author_sort	Jaume Llibre
title	A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
title_short	A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
title_full	A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
title_fullStr	A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
title_full_unstemmed	A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
title_sort	note on the first integrals of vector fields with integrating factors and normalizers
publisher	National Academy of Science of Ukraine
series	Symmetry, Integrability and Geometry: Methods and Applications
issn	1815-0659
publishDate	2012-06-01
description	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.
topic	first integral vector field integrating factor normalizer
url	http://dx.doi.org/10.3842/SIGMA.2012.035
work_keys_str_mv	AT jaumellibre anoteonthefirstintegralsofvectorfieldswithintegratingfactorsandnormalizers AT danielperaltasalas anoteonthefirstintegralsofvectorfieldswithintegratingfactorsandnormalizers AT jaumellibre noteonthefirstintegralsofvectorfieldswithintegratingfactorsandnormalizers AT danielperaltasalas noteonthefirstintegralsofvectorfieldswithintegratingfactorsandnormalizers
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A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers

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