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Symmetry, Integrability and Geometry: Methods and Applications, 2012, Volume 8, 035, 9 pp.
DOI: https://doi.org/10.3842/SIGMA.2012.035
(Mi sigma712)
 

This article is cited in 8 scientific papers (total in 8 papers)

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

Jaume Llibrea, Daniel Peralta-Salasb

a Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain
b Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, C. Nicolás Cabrera 13-15, 28049 Madrid, Spain
Full-text PDF (323 kB) Citations (8)
References:
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, vector field, integrating factor, normalizer.
Received: February 16, 2012; in final form June 12, 2012; Published online June 14, 2012
Bibliographic databases:
Document Type: Article
MSC: 34C05, 34A34, 34C14
Language: English
Citation: Jaume Llibre, Daniel Peralta-Salas, “A note on the first integrals of vector fields with integrating factors and normalizers”, SIGMA, 8 (2012), 035, 9 pp.
Citation in format AMSBIB
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\paper A note on the first integrals of vector fields with integrating factors and normalizers
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  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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