An extension of Sharkovsky's theorem to periodic difference equations

Ziyad AlSharawi, James Angelos, Saber Elaydi, Leela Rakesh

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


We present an extension of Sharkovsky's theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric cycle with or without stability properties.

Original languageEnglish
Pages (from-to)128-141
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Apr 1 2006


  • Difference equations
  • Geometric cycles
  • Nonautonomous
  • Periodic orbits
  • Skew-product dynamical systems


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