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On planar polynomial vector fields with elementary first integrals

Author
Christopher, C.; Llibre, J.; Panzati, C.; Walcher, S.
Type of activity
Journal article
Journal
Journal of differential equations
Date of publication
2019-10-05
Volume
267
Number
8
First page
4572
Last page
4588
DOI
10.1016/j.jde.2019.05.007
URL
https://www.sciencedirect.com/science/article/pii/S0022039619302128 Open in new window
Abstract
We show that under rather general conditions a polynomial differential system having an elementary first integral already must admit a Darboux first integral, and we explicitly characterize the vector fields in this class. We also investigate some exceptional cases, i.e. equations admitting an elementary first integral but not a Darboux first integral. In particular we provide a rather detailed discussion of exceptional elementary first integrals built from algebraic functions of prime degree.

Participants

  • Christopher, Colin  (author)
  • Llibre Saló, Jaume  (author)
  • Panzati, Chara  (author)
  • Walcher, Sebastian  (author)