Algebraic Limit Cycles on Quadratic Polynomial Differential Systems

Jaume Llibre, Claudia Valls

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1 Citation (Scopus)

Abstract

© 2018 Edinburgh Mathematical Society. Algebraic limit cycles in quadratic polynomial differential systems started to be studied in 1958, and a few years later the following conjecture appeared: quadratic polynomial differential systems have at most one algebraic limit cycle. We prove that a quadratic polynomial differential system having an invariant algebraic curve with at most one pair of diametrically opposite singular 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)499-512
JournalProceedings of the Edinburgh Mathematical Society
Volume61
Issue number2
DOIs
Publication statusPublished - 1 May 2018

Keywords

  • algebraic limit cycle
  • quadratic polynomial differential system
  • quadratic polynomial vector field

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