Limit cycles, invariant meridians and parallels for polynomial vector fields on the torus

Jaume Llibre, João C. Medrado

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5 Citations (Scopus)

Abstract

We study the polynomial vector fields of arbitrary degree in R3 having the 2-dimensional torus. with a>1, invariant by their flow. We characterize all the possible configurations of invariant meridians and parallels that these vector fields can exhibit. Furthermore we analyze when these invariant either meridians or parallels can be limit cycles. © 2010 Elsevier Masson SAS.
Original languageEnglish
Pages (from-to)1-9
JournalBulletin des Sciences Mathematiques
Volume135
Issue number1
DOIs
Publication statusPublished - 1 Jan 2011

Keywords

  • Invariant meridian
  • Invariant parallel
  • Limit cycle
  • Periodic orbit
  • Polynomial vector fields

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