Counterexample to a conjecture on the algebraic limit cycles of polynomial vector fields

Jaume Llibre, Chara Pantazi

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

In Geometriae Dedicata 79 (2000), 101-108, Rudolf Winkel conjectured: for a given algebraic curve f=0 of degree m ≥ 4 there is in general no polynomial vector field of degree less than 2m -1 leaving invariant f=0 and having exactly the ovals of f=0 as limit cycles. Here we show that this conjecture is not true. © Springer 2005.
Original languageEnglish
Pages (from-to)213-219
JournalGeometriae Dedicata
Volume110
DOIs
Publication statusPublished - 1 Feb 2005

Keywords

  • Algebraic limit cycles
  • Polynomial vector fields

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