On the remarkable values of the rational first integrals of polynomial vector fields

Antoni Ferragut, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

20 Citations (Scopus)

Abstract

The remarkable values for polynomial vector fields in the plane having a rational first integral were introduced by Poincaré. He was mainly interested in their algebraic aspects. Here we are interested in their dynamic aspects; i.e. how they contribute to the phase portrait of the system, to its separatrices, to its singular points, etc. The relationship between remarkable values and dynamics mainly takes place through the inverse integrating factor. © 2007 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)399-417
JournalJournal of Differential Equations
Volume241
DOIs
Publication statusPublished - 15 Oct 2007

Keywords

  • First integral
  • Inverse integrating factor
  • Polynomial vector field
  • Remarkable value

Fingerprint Dive into the research topics of 'On the remarkable values of the rational first integrals of polynomial vector fields'. Together they form a unique fingerprint.

Cite this