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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2012 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148427 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862645031687421952 |
|---|---|
| author | Llibre, J. Peralta-Salas, D. |
| author_facet | Llibre, J. Peralta-Salas, D. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-01T10:10:16Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148427 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T10:10:16Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers Llibre, J. Peralta-Salas, D. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148427 |
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