On the uniqueness of algebraic limit cycles for quadratic polynomial differential systems with two pairs of equilibrium points at infinity

Jaume Llibre, Claudia Valls

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

© 2017, Springer Science+Business Media Dordrecht. Algebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and few years later the following conjecture appeared: quadratic polynomial differential systems have at most one algebraic limit cycle. We prove that for a quadratic polynomial differential system having two pairs of diametrally opposite equilibrium points at infinity, has at most one algebraic limit cycle. Our result provides a partial positive answer to this conjecture.
Original languageEnglish
Pages (from-to)37-52
JournalGeometriae Dedicata
Volume191
Issue number1
DOIs
Publication statusPublished - 1 Dec 2017

Keywords

  • Algebraic limit cycle
  • Quadratic polynomial differential system
  • Quadratic polynomial vector field

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