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

Jaume Llibre, Daniel Peralta-Salas

Research output: Contribution to journalArticleResearchpeer-review

4 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 languageEnglish
Article number035
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume8
DOIs
Publication statusPublished - 1 Dec 2012

Keywords

  • First integral
  • Integrating factor
  • Normalizer
  • Vector field

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