Limit cycles of linear vector fields on manifolds

Jaume Llibre, Xiang Zhang

Research output: Contribution to journalArticleResearchpeer-review


© 2016 IOP Publishing Ltd and London Mathematical Society. It is well known that linear vector fields on the manifold ℝn cannot have limit cycles, but this is not the case for linear vector fields on other manifolds. We study the periodic orbits of linear vector fields on different manifolds, and motivate and present an open problem on the number of limit cycles of linear vector fields on a class of C1 connected manifold.
Original languageEnglish
Pages (from-to)3120-3131
Issue number10
Publication statusPublished - 26 Aug 2016


  • averaging method
  • centre
  • isochronous centre
  • limit cycle
  • periodic orbit


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