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A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік
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A Note on the First Integrals of Vector Fields with Integrating Factors and Normalizers
Інший ID:
2010 Mathematics Subject Classification: 34C05; 34A34; 34C14
DOI: http://dx.doi.org/10.3842/SIGMA.2012.035
DOI: http://dx.doi.org/10.3842/SIGMA.2012.035
Посилання:
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.
Підтримка:
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.
Дата:
2012
Переглядів:
613
Завантажень:
248
Анотація:
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.
