Folding and unfolding in periodic difference equations

Ziyad AlSharawi; Jose Cánovas; Antonio Linero

doi:10.1016/j.jmaa.2014.03.060

Folding and unfolding in periodic difference equations

Ziyad AlSharawi^*, Jose Cánovas, Antonio Linero

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Given a p-periodic difference equation x_n+1=f_nmodp(x_n), where each f_j 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 language	English
Pages (from-to)	643-659
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	417
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2014.03.060
Publication status	Published - Sept 15 2014

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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10.1016/j.jmaa.2014.03.060

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@article{0d0c874f4af144bb8ee0335ec4a017be,

title = "Folding and unfolding in periodic difference equations",

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.",

keywords = "Alternating systems, Cycles, Folding, Interval maps, Non-autonomous difference equations, Periodic solutions, Periods, Unfolding",

author = "Ziyad AlSharawi and Jose C{\'a}novas and Antonio Linero",

note = "Funding Information: The second and third authors were supported by Grant MTM2011-23221 , Ministerio de Ciencia e Innovaci{\'o}n, Spain , and by Grant 08667/PI/08 , Programa de Generaci{\'o}n de Conocimiento Cient{\'i}fico de Excelencia de la Fundaci{\'o}n S{\'e}neca , Agencia de Ciencia y Tecnolog{\'i}a de la Comunidad Aut{\'o}noma de la Regi{\'o}n de Murcia (II PCTRM 2007-10).",

year = "2014",

month = sep,

day = "15",

doi = "10.1016/j.jmaa.2014.03.060",

language = "English",

volume = "417",

pages = "643--659",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

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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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DO - 10.1016/j.jmaa.2014.03.060

M3 - Article

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SN - 0022-247X

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EP - 659

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Folding and unfolding in periodic difference equations

Abstract

Keywords

ASJC Scopus subject areas

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