The Poincaré center problem

Henryk Zoła̧dek, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

14 Citations (Scopus)


We present two examples of real planar polynomial vector fields with an orbitally linearizable saddle point such that they are neither rationally reversible nor Liouvillian integrable. We show that vector fields from one of these examples form an isolated component of the so-called integrable saddle variety. Next, we discuss the problem of partial duality between real centers and real integrable saddles and the problem of continuous moduli for the center variety. © Springer Science+Business Media, LLC 2008.
Original languageEnglish
Pages (from-to)505-535
JournalJournal of Dynamical and Control Systems
Issue number4
Publication statusPublished - 16 Oct 2008


  • Center
  • Integrable saddle
  • Polynomial vector field


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