Invariant hyperplanes and Darboux integrability for d -dimensional polynomial differential systems

Jaume Llibre, Gerardo Rodríguez

Research output: Contribution to journalArticleResearchpeer-review

15 Citations (Scopus)

Abstract

For a class of polynomial differential systems of degree (m1,...,md) in Rd which is open and dense in the set of all polynomial differential systems of degree (m1,...,md) in Rd, we study the maximal number of invariant hyperplanes. This is a well known problem in dimension d=2 (see for instance [1,12,16]). Furthermore, using the Darboux theory of integrability we analyse when can be possible to find a first integral of a polynomial vector field of degree (m1,...,md) in Rd by knowing the existence of a sufficient number of invariant hyperplanes. © 2000 Elsevier, Paris.
Original languageEnglish
Pages (from-to)599-619
JournalBulletin des Sciences Mathematiques
Volume124
DOIs
Publication statusPublished - 1 Jan 2000

Keywords

  • 34C05
  • 58F14
  • 58F22
  • Darboux integrability
  • Invariant hyperplane
  • Polynomial differential system

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