Polynomial vector fields in ℝ3 with infinitely many limit cycles

Antoni Ferragut, Jaume Llibre, Chara Pantazi

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2 Citations (Scopus)

Abstract

We provide a constructive method to obtain polynomial vector fields in ℝ3 having infinitely many limit cycles starting from polynomial vector fields in ℝ2 with a period annulus. We present two examples of polynomial vector fields in ℝ3 having infinitely many limit cycles, one of them of degree 2 and the other one of degree 12. The main tools of our method are the Melnikov integral and the Hamiltonian structure. © 2013 World Scientific Publishing Company.
Original languageEnglish
Article number1350029
JournalInternational Journal of Bifurcation and Chaos
Volume23
Issue number2
DOIs
Publication statusPublished - 1 Jan 2013

Keywords

  • Limit cycle
  • Melnikov integral

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    Ferragut, A., Llibre, J., & Pantazi, C. (2013). Polynomial vector fields in ℝ3 with infinitely many limit cycles. International Journal of Bifurcation and Chaos, 23(2), [1350029]. https://doi.org/10.1142/S0218127413500296