On the period function for a family of complex differential equations

Armengol Gasull Embid, Antonio Garijo, Xavier Jarque

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

Abstract

We consider planar differential equations of the form over(z, ̇) = f ( z ) g ( over(z, -) ) being f ( z ) and g ( z ) holomorphic functions and prove that if g ( z ) is not constant then for any continuum of period orbits the period function has at most one isolated critical period, which is a minimum. Among other implications, the paper extends a well-known result for meromorphic equations, over(z, ̇) = h ( z ), that says that any continuum of periodic orbits has a constant period function. © 2005 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)314-331
JournalJournal of Differential Equations
Volume224
DOIs
Publication statusPublished - 15 May 2006

Keywords

  • Critical period
  • Meromorphic vector fields
  • Period function
  • Periodic orbit

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