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Counterexample to a Conjecture on the Algebraic Limit Cycles of Polynomial Vector Fields

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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.

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Authors and Affiliations

  1. Departament de Matemátiques, Universitat Autónoma de Barcelona, Bellaterra, Barcelona, Spain, 08193

    Jaume Llibre & Chara Pantazi

Authors
  1. Jaume Llibre
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  2. Chara Pantazi
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Correspondence to Jaume Llibre.

Additional information

Mathematics Subject Classifications (2000). Primary 14P25, 34C05, 34A34.

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Llibre, J., Pantazi, C. Counterexample to a Conjecture on the Algebraic Limit Cycles of Polynomial Vector Fields. Geom Dedicata 110, 213–219 (2005). https://doi.org/10.1007/s10711-004-2454-3

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  • DOI: https://doi.org/10.1007/s10711-004-2454-3

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