A note on the first integrals of vector fields with integrating factors and normalizers

Jaume Llibre; Daniel Peralta-Salas

doi:10.3842/SIGMA.2012.035

A note on the first integrals of vector fields with integrating factors and normalizers

Jaume Llibre, Daniel Peralta-Salas

Departament de Matemàtiques

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Resum

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.

Idioma original	Anglès
Número d’article	035
Revista	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volum	8
DOIs	https://doi.org/10.3842/SIGMA.2012.035
Estat de la publicació	Publicada - 1 de des. 2012

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10.3842/SIGMA.2012.035

https://ddd.uab.cat/record/150493

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https://www.scopus.com/pages/publications/84882319846

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@article{35c04705301d455ab72a49b6e85cfab8,

title = "A note on the first integrals of vector fields with integrating factors and normalizers",

abstract = "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.",

keywords = "First integral, Integrating factor, Normalizer, Vector field",

author = "Jaume Llibre and Daniel Peralta-Salas",

year = "2012",

month = dec,

day = "1",

doi = "10.3842/SIGMA.2012.035",

language = "English",

volume = "8",

journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",

issn = "1815-0659",

publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}

TY - JOUR

T1 - A note on the first integrals of vector fields with integrating factors and normalizers

AU - Llibre, Jaume

AU - Peralta-Salas, Daniel

PY - 2012/12/1

Y1 - 2012/12/1

N2 - 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.

AB - 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.

KW - First integral

KW - Integrating factor

KW - Normalizer

KW - Vector field

UR - https://www.scopus.com/pages/publications/84882319846

U2 - 10.3842/SIGMA.2012.035

DO - 10.3842/SIGMA.2012.035

M3 - Article

SN - 1815-0659

VL - 8

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

M1 - 035

ER -

A note on the first integrals of vector fields with integrating factors and normalizers

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