Phase portraits and invariant straight lines of cubic polynomial vector fields having a quadratic rational first integral

Jaume Llibre, Adam Mahdi, Nicolae Vulpe

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)

Abstract

In this paper we classify all cubic polynomial differential systems having a rational first integral of degree two. In other words we characterize all the global phase portraits of the cubic polynomial differential systems having all their orbits contained in conies. We also determine their configurations of invariant straight lines. We show that there are exactly 38 topologically different phase portraits in the Poincare' disc associated with this family of cubic polynomial differential systems up to a reversed sense of their orbits. Copyright © 2011 Rocky Mountain Mathematics Consortium.
Original languageEnglish
Pages (from-to)1585-1629
JournalRocky Mountain Journal of Mathematics
Volume41
DOIs
Publication statusPublished - 25 Nov 2011

Keywords

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

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