Configurations of limit cycles and planar polynomial vector fields

Jaume Llibre, Gerardo Rodríguez

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53 Citations (Scopus)

Abstract

We show that every finite configuration of disjoint simple closed curves of the plane is topologically realizable as the set of limit cycles of a polynomial vector field. Moreover, the realization can be made by algebraic limit cycles, and we provide an explicit polynomial vector field exhibiting any given finite configuration of limit cycles. © 2003 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)374-380
JournalJournal of Differential Equations
Volume198
DOIs
Publication statusPublished - 10 Apr 2004

Keywords

  • Limit cycles
  • Quadratic vector fields

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    Llibre, J., & Rodríguez, G. (2004). Configurations of limit cycles and planar polynomial vector fields. Journal of Differential Equations, 198, 374-380. https://doi.org/10.1016/j.jde.2003.10.008