Limit cycles bifurcating from the period annulus of quasi-Homogeneous centers

Weigu Li, Jaume Llibre, Jiazhong Yang, Zhifen Zhang

Research output: Contribution to journalArticleResearchpeer-review

37 Citations (Scopus)

Abstract

We provide upper bounds for the maximum number of limit cycles bifurcating from the period annulus of any homogeneous and quasi-homogeneous center, which can be obtained using the Abelian integral method of first order. We show that these bounds are the best possible using the Abelian integral method of first order. We note that these centers are in general non-Hamiltonian. As a consequence of our study we provide the biggest known number of limit cycles surrounding a unique singular point in terms of the degree n of the system for arbitrary large n. © 2008 Springer Science+Business Media, LLC.
Original languageEnglish
Pages (from-to)133-152
JournalJournal of Dynamics and Differential Equations
Volume21
DOIs
Publication statusPublished - 1 Mar 2009

Keywords

  • Homogeneous centers
  • Limit cycles
  • Quasi-homogeneous centers

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