Limit cycles from a four-dimensional centre in ℝ m in resonance p : q

Luis Barreira, Jaume Llibre, Claudia Valls

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

Given positive coprime integers p and q, we consider the linear differential centre in ℝ m with eigenvalues ±pi, ±qi and 0 with multiplicity m-4. We perturb this linear centre in the class of all polynomial differential systems of the form linear plus a homogeneous nonlinearity of degree p+q-1, i.e., ẋ = Ax+εF(x), where every component of F(x) is a linear polynomial plus a homogeneous polynomial of degree p+q-1. When the displacement function of order 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 centre. © 2012 Copyright Taylor and Francis Group, LLC.
Original languageEnglish
Pages (from-to)459-474
JournalDynamical Systems
Volume27
Issue number4
DOIs
Publication statusPublished - 1 Dec 2012

Keywords

  • averaging theory
  • limit cycles
  • periodic orbit
  • resonance p : q

Fingerprint Dive into the research topics of 'Limit cycles from a four-dimensional centre in ℝ <sup>m</sup> in resonance p : q'. Together they form a unique fingerprint.

Cite this