### 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 |
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Pages (from-to) | 643-659 |

Number of pages | 17 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 417 |

Issue number | 2 |

DOIs | |

Publication status | Published - Sep 15 2014 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*417*(2), 643-659. https://doi.org/10.1016/j.jmaa.2014.03.060

**Folding and unfolding in periodic difference equations.** / AlSharawi, Ziyad; Cánovas, Jose; Linero, Antonio.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 417, no. 2, pp. 643-659. https://doi.org/10.1016/j.jmaa.2014.03.060

}

TY - JOUR

T1 - Folding and unfolding in periodic difference equations

AU - AlSharawi, Ziyad

AU - Cánovas, Jose

AU - Linero, Antonio

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

UR - http://www.scopus.com/inward/record.url?scp=84899080294&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84899080294&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2014.03.060

DO - 10.1016/j.jmaa.2014.03.060

M3 - Article

VL - 417

SP - 643

EP - 659

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -