Invariant Parallels, Invariant Meridians and Limit Cycles of Polynomial Vector Fields on Some 2-Dimensional Algebraic Tori in ℝ3

Jaume Llibre, Salomón Rebollo-Perdomo

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5 Citations (Scopus)

Abstract

We consider the polynomial vector fields of arbitrary degree in ℝ3 having the 2-dimensional algebraic torus, where l, m and n positive integers, and r ∈ (1, ∞), invariant by their flow. We study the possible configurations of invariant meridians and parallels that these vector fields can exhibit on T2(l, m, n). Furthermore, we analyze when these invariant meridians or parallels are limit cycles. © 2013 Springer Science+Business Media New York.
Original languageEnglish
Pages (from-to)777-793
JournalJournal of Dynamics and Differential Equations
Volume25
Issue number3
DOIs
Publication statusPublished - 1 Sep 2013

Keywords

  • 2-Dimensional torus
  • Invariant meridian
  • Invariant parallel
  • Limit cycle
  • Periodic orbit
  • Polynomial vector field

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