Normal forms for polynomial differential systems in R3 having an invariant quadric and a darboux invariant

Jaume Llibre, Marcelo Messias, Alisson De Carvalho Reinol

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

© 2015 World Scientific Publishing Company. We give the normal forms of all polynomial differential systems in R3 which have a nondegenerate or degenerate quadric as an invariant algebraic surface. We also characterize among these systems those which have a Darboux invariant constructed uniquely using the invariant quadric, giving explicitly their expressions. As an example, we apply the obtained results in the determination of the Darboux invariants for the Chen system with an invariant quadric.
Original languageEnglish
Article number1550015
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume25
Issue number1
DOIs
Publication statusPublished - 25 Jan 2015

Keywords

  • Darboux integrability
  • Darboux invariant
  • Polynomial differential systems
  • invariant quadric

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