TY - JOUR

T1 - Folding and unfolding in periodic difference equations

AU - AlSharawi, Ziyad

AU - Cánovas, Jose

AU - Linero, Antonio

N1 - Funding Information:
The second and third authors were supported by Grant MTM2011-23221 , Ministerio de Ciencia e Innovación, Spain , and by Grant 08667/PI/08 , Programa de Generación de Conocimiento Científico de Excelencia de la Fundación Séneca , Agencia de Ciencia y Tecnología de la Comunidad Autónoma de la Región de Murcia (II PCTRM 2007-10).

PY - 2014/9/15

Y1 - 2014/9/15

N2 - 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.

AB - 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.

KW - Alternating systems

KW - Cycles

KW - Folding

KW - Interval maps

KW - Non-autonomous difference equations

KW - Periodic solutions

KW - Periods

KW - Unfolding

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U2 - 10.1016/j.jmaa.2014.03.060

DO - 10.1016/j.jmaa.2014.03.060

M3 - Article

AN - SCOPUS:84899080294

SN - 0022-247X

VL - 417

SP - 643

EP - 659

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -