Darbouxian integrability of polynomial vector fields with special emphasis on the two-dimensional surfaces

Jaume Llibre, Gerardo Rodríguez

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

A survey on the Darbouxian theory of integrability for real polynomial vector fields in the plane is presented. The theory is then extended to real polynomial vector fields on two-dimensional surfaces, more specifically on the quadratics and on the two-dimensional torus. The notion of a polynomial vector field on a regular surface and the notion of a first integral for such vector fields are defined.
Original languageEnglish
Pages (from-to)2821-2833
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume12
DOIs
Publication statusPublished - 1 Jan 2002

Keywords

  • Integrability
  • Polynomial vector fields

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