Limit cycles of resonant four-dimensional polynomial systems

Jaume Llibre, Ana Cristina Mereu, Marco A. Teixeira

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)


We study the bifurcation of limit cycles from four-dimensional centres inside a class of polynomial differential systems. Our results establish an upper bound for the number of limit cycles which can be prolonged in function of the degree of the polynomial perturbation considered, up to first-order expansion of the displacement function with respect to small parameter. The main tool for proving such results is the averaging theory. © 2010 Taylor & Francis.
Original languageEnglish
Pages (from-to)145-158
JournalDynamical Systems
Issue number2
Publication statusPublished - 1 Jun 2010


  • Averaging theory
  • Limit cycle
  • Periodic orbit
  • Resonance


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