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Folding and unfolding in periodic difference equations
Al-Sharawi, Ziyad Cánovas, Jose Linero, Antonio
Al-Sharawi, Ziyad
Cánovas, Jose
Linero, Antonio
Date
2014
Advisor
Type
Peer-Reviewed
Article
Preprint
Article
Preprint
Degree
Description
Abstract
Given a p-periodic difference equation xn+1 = fn mod p(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.