Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2

Laurent Cairó, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

26 Citations (Scopus)

Abstract

We classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 2. In other words we characterize all the global phase portraits of the quadratic polynomial vector fields having all their orbits contained in conics. For such a vector field there are exactly 25 different global phase portraits in the Poincaré disc, up to a reversal of sense. © 2006 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)327-348
JournalNonlinear Analysis, Theory, Methods and Applications
Volume67
DOIs
Publication statusPublished - 15 Jul 2007

Keywords

  • Integrability
  • Phase portraits
  • Quadratic vector fields
  • Rational first integral

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