Folding and unfolding in periodic difference equations

Ziyad AlSharawi, Jose Cánovas, Antonio Linero

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Given a p-periodic difference equation xn+1=fnmodp(xn), where each fj is a continuous interval map, j=0, 1,.. ., p-1, we discuss the notion of folding and unfolding related to this type of non-autonomous equations. It is possible to glue certain maps of this equation to shorten its period, which we call folding. On the other hand, we can unfold the glued maps so the original structure can be recovered or understood. Here, we focus on the periodic structure under the effect of folding and unfolding. In particular, we analyze the relationship between the periods of periodic sequences of the p-periodic difference equation and the periods of the corresponding subsequences related to the folded systems.

Original languageEnglish
Pages (from-to)643-659
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume417
Issue number2
DOIs
Publication statusPublished - Sep 15 2014

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Keywords

  • Alternating systems
  • Cycles
  • Folding
  • Interval maps
  • Non-autonomous difference equations
  • Periodic solutions
  • Periods
  • Unfolding

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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