Darboux integrability of real polynomial vector fields on regular algebraic hypersurfaces

Jaume Llibre, Xiang Zhang

Research output: Contribution to journalArticleResearchpeer-review

17 Citations (Scopus)

Abstract

In this paper we extend the Darboux theory of integrability in ℝ n to the regular algebraic hypersurfaces. Then we apply the extended theory first to the 3-dimensional generalized cylinders (S 1) × ℝ 3-r of ℝ 4 for r=0, 1, 2, 3; and after to then-dimensional sphere S n of ℝ n+1. © 2002 Springer.
Original languageEnglish
Pages (from-to)109-126
JournalRendiconti del Circolo Matematico di Palermo
Volume51
DOIs
Publication statusPublished - 1 Feb 2002

Keywords

  • Darboux integrability
  • generalized cylinder
  • sphere
  • torus

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