A note on the period function for certain planar vector fields

Antonio Garijo, Armengol Gasull, Xavier Jarque

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

Consider a smooth planar autonomous differential equation having a period annulus, P. We present a new criterion to ensure that the period function has at most one critical period on P. Our result has a compact form when the differential equation is written as ż = F(z, z̄). It is based on a suitable representation formula of the derivative of the period function which uses the infinitesimal generator associated to the continua of periodic orbits. We apply the criterion to several particular cases of the equation ż = f(z)g(z̄)/h(z, z̄), where f(z) and are holomorphic functions and h is a C2 smooth real valuated function. © 2010 Taylor & Francis.
Original languageEnglish
Pages (from-to)631-645
JournalJournal of Difference Equations and Applications
Volume16
Issue number5
DOIs
Publication statusPublished - 1 May 2010

Keywords

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

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