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SIGMA, 2012, Volume 8, 035, 9 pages (Mi sigma712)  

This article is cited in 4 scientific papers (total in 4 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

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.

DOI: https://doi.org/10.3842/SIGMA.2012.035

Full text: PDF file (323 kB)
Full text: http://emis.mi.ras.ru/.../035
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Bibliographic databases:

ArXiv: 1206.3005
MSC: 34C05, 34A34, 34C14
Received: February 16, 2012; in final form June 12, 2012; Published online June 14, 2012
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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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\by Jaume Llibre, Daniel Peralta-Salas
\paper A note on the first integrals of vector fields with integrating factors and normalizers
\jour SIGMA
\yr 2012
\vol 8
\papernumber 035
\totalpages 9
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Buica A., Garcia I.A., Maza S., “Inverse Jacobi Multipliers: Recent Applications in Dynamical Systems”, Progress and Challenges in Dynamical Systems, Springer Proceedings in Mathematics & Statistics, 54, eds. Ibanez S., DelRio J., Pumarino A., Rodriguez J., Springer-Verlag Berlin, 2013, 127–141  crossref  mathscinet  zmath  isi  scopus
    2. Ballesteros A. Blasco A. Herranz F.J. de Lucas J. Sardon C., “Lie-Hamilton Systems on the Plane: Properties, Classification and Applications”, J. Differ. Equ., 258:8 (2015), 2873–2907  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Garcia I.A., “Complete Integrability, Orbital Linearizability and Independent Normalizers For Local Vector Fields in R-N”, J. Lie Theory, 25:1 (2015), 37–43  mathscinet  zmath  isi
    4. Hu Ya., “On the First Integrals of N-Th Order Autonomous Systems”, J. Math. Anal. Appl., 459:2 (2018), 1062–1078  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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