An extension of Sharkovsky's theorem to periodic difference equations

Ziyad AlSharawi, James Angelos, Saber Elaydi, Leela Rakesh

Research output: Contribution to journalArticle

44 Citations (Scopus)

Abstract

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
Volume316
Issue number1
DOIs
Publication statusPublished - Apr 1 2006

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Difference equations
Difference equation
Theorem
Converse
Cycle

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

An extension of Sharkovsky's theorem to periodic difference equations. / AlSharawi, Ziyad; Angelos, James; Elaydi, Saber; Rakesh, Leela.

In: Journal of Mathematical Analysis and Applications, Vol. 316, No. 1, 01.04.2006, p. 128-141.

Research output: Contribution to journalArticle

AlSharawi, Ziyad ; Angelos, James ; Elaydi, Saber ; Rakesh, Leela. / An extension of Sharkovsky's theorem to periodic difference equations. In: Journal of Mathematical Analysis and Applications. 2006 ; Vol. 316, No. 1. pp. 128-141.
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