Orbitally symmetric systems with applications to planar centers

Jefferson L.R. Bastos, Claudio Aguinaldo Buzzi, Joan Torregrosa*

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)


We present a generalization of the most usual symmetries in differential equations known as the time-reversibility and the equivariance ones. We check that the typical properties are also valid for the new definition that unifies both. With it, we are able to present new families of planar polynomial vector fields having equilibrium points of center type. Moreover, we provide the highest lower bound for the local cyclicity of an equilibrium point of polynomial vector fields of degree 6; M(6) ≥ 48.

Original languageEnglish
Pages (from-to)3301-3329
Number of pages29
JournalCommunications on Pure and Applied Analysis
Issue number10
Publication statusPublished - Oct 2021


  • Centers
  • Equivariance
  • Involution
  • Limit cycles
  • Local cyclicity
  • Reversibility
  • Symmetry


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