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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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2012
Hauptverfasser: Llibre, J., Peralta-Salas, D.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2012
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/148427
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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record_format dspace
spelling Llibre, J.
Peralta-Salas, D.
2019-02-18T12:15:20Z
2019-02-18T12:15:20Z
2012
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.
1815-0659
2010 Mathematics Subject Classification: 34C05; 34A34; 34C14
DOI: http://dx.doi.org/10.3842/SIGMA.2012.035
https://nasplib.isofts.kiev.ua/handle/123456789/148427
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.
The authors acknowledge three referees for corrections and comments which have helped to improve the presentation of this paper. J.Ll. is partially supported by a MICINN/FEDER grant no. MTM2008–03437, by an AGAUR grant no. 2009SGR-410 and by ICREA Academia. D.P.-S. is supported by a MICINN grant no. MTM2010–21186-C02-01, by the ICMAT Severo Ochoa grant no. SEV-2011-0087 and by the Ram´on y Cajal program.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
spellingShingle A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
Llibre, J.
Peralta-Salas, D.
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
author Llibre, J.
Peralta-Salas, D.
author_facet Llibre, J.
Peralta-Salas, D.
publishDate 2012
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/148427
citation_txt 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.
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