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

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

6 Citations (Scopus)

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.

Original language	English
Article number	035
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	8
DOIs	https://doi.org/10.3842/SIGMA.2012.035
Publication status	Published - 1 Dec 2012

Keywords

First integral
Integrating factor
Normalizer
Vector field

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10.3842/SIGMA.2012.035

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

Cite this

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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.",

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AU - Peralta-Salas, Daniel

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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

Abstract

Keywords

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