Analytic reducibility of nondegenerate centers: Cherkas systems

Jaume Giné, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)


© 2016, University of Szeged. All Rights Reserved. In this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. We also study the centers for the Cherkas polynomial differential systems (Formula Presented), where Pi(x) are polynomials of degree n, P0(0) = 0 and P0′(0) < 0. Computing the focal values we find the center conditions for such systems for degree 3, and using modular arithmetics for degree 4. Finally we do a conjecture about the center conditions for Cherkas polynomial differential systems of degree n.
Original languageEnglish
Article number49
JournalElectronic Journal of Qualitative Theory of Differential Equations
Publication statusPublished - 1 Jan 2016


  • Analytic integrability
  • Center problem
  • Polynomial cherkas differential systems


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