### 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 |

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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

### Cite this

*Journal of Mathematical Analysis and Applications*,

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