Bifurcation of limit cycles from a 4-dimensional center in R{double-struck} m in resonance 1:N

Luis Barreira, Jaume Llibre, Claudia Valls

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12 Citations (Scopus)

Abstract

For every positive integer N≥. 2 we consider the linear differential center x ̇=Ax in R{double-struck} m with eigenvalues ±i, ± Ni and 0 with multiplicity m-4. We perturb this linear center inside the class of all polynomial differential systems of the form linear plus a homogeneous nonlinearity of degree N, i.e. x ̇=Ax+εF(x) where every component of F(x) is a linear polynomial plus a homogeneous polynomial of degree N. When the displacement function of order ε of the perturbed system is not identically zero, we study the maximal number of limit cycles that can bifurcate from the periodic orbits of the linear differential center. In particular, we give explicit upper bounds for the number of limit cycles. © 2011 Elsevier Inc.
Original languageEnglish
Pages (from-to)754-768
JournalJournal of Mathematical Analysis and Applications
Volume389
Issue number2
DOIs
Publication statusPublished - 15 May 2012

Keywords

  • Averaging theory
  • Limit cycles
  • Periodic orbit
  • Resonance 1:N

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