Centers and Isochronous Centers for Two Classes of Generalized Seventh and Ninth Systems

Jaume Llibre, Clàudia Valls

Research output: Contribution to journalArticleResearchpeer-review

8 Citations (Scopus)

Abstract

We classify new classes of centers and of isochronous centers for polynomial differential systems in ℝ2 of arbitrary odd degree d ≥ 7 that in complex notation z = x + iy can be written as where j is either 0 or 1, λ ε ℝ and A,B,C ε ℂ. Note that if j = 0 and d = 7 we obtain a special case of seventh polynomial differential systems which can have a center at the origin, and if j = 1 and d = 9 we obtain a special case of ninth polynomial differential systems which can have a center at the origin. © 2010 Springer Science+Business Media, LLC.
Original languageEnglish
Pages (from-to)657-675
JournalJournal of Dynamics and Differential Equations
Volume22
Issue number4
DOIs
Publication statusPublished - 1 Apr 2010

Keywords

  • Centers
  • Isochronous
  • Polynomial vector fields

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