### Abstract

In this paper, we characterize periodic solutions of p-periodic difference equations. We classify the periods into multiples of p and nonmultiples of p. We show that the elements of the set of multiples of p follow the well-known Sharkovsky's ordering multiplied by p. On the other hand, we show that the elements of the set Γ_{p} of nonmultiples of p are independent in their existence. Moreover, we show the existence of a p-periodic difference equation with infinite Γ_{p}-set in which the maps are defined on a compact domain and agree exactly on a countable set. Based on the proposed classification, we give a refinement of Sharkovsky's theorem for periodic difference equations.

Original language | English |
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Pages (from-to) | 921-928 |

Number of pages | 8 |

Journal | Chaos, Solitons and Fractals |

Volume | 44 |

Issue number | 11 |

DOIs | |

Publication status | Published - Nov 2011 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Chaos, Solitons and Fractals*,

*44*(11), 921-928. https://doi.org/10.1016/j.chaos.2011.07.011

**A new characterization of periodic oscillations in periodic difference equations.** / Al-Salman, Ahmad; Alsharawi, Ziyad.

Research output: Contribution to journal › Article

*Chaos, Solitons and Fractals*, vol. 44, no. 11, pp. 921-928. https://doi.org/10.1016/j.chaos.2011.07.011

}

TY - JOUR

T1 - A new characterization of periodic oscillations in periodic difference equations

AU - Al-Salman, Ahmad

AU - Alsharawi, Ziyad

PY - 2011/11

Y1 - 2011/11

N2 - In this paper, we characterize periodic solutions of p-periodic difference equations. We classify the periods into multiples of p and nonmultiples of p. We show that the elements of the set of multiples of p follow the well-known Sharkovsky's ordering multiplied by p. On the other hand, we show that the elements of the set Γp of nonmultiples of p are independent in their existence. Moreover, we show the existence of a p-periodic difference equation with infinite Γp-set in which the maps are defined on a compact domain and agree exactly on a countable set. Based on the proposed classification, we give a refinement of Sharkovsky's theorem for periodic difference equations.

AB - In this paper, we characterize periodic solutions of p-periodic difference equations. We classify the periods into multiples of p and nonmultiples of p. We show that the elements of the set of multiples of p follow the well-known Sharkovsky's ordering multiplied by p. On the other hand, we show that the elements of the set Γp of nonmultiples of p are independent in their existence. Moreover, we show the existence of a p-periodic difference equation with infinite Γp-set in which the maps are defined on a compact domain and agree exactly on a countable set. Based on the proposed classification, we give a refinement of Sharkovsky's theorem for periodic difference equations.

UR - http://www.scopus.com/inward/record.url?scp=80054042435&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80054042435&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2011.07.011

DO - 10.1016/j.chaos.2011.07.011

M3 - Article

VL - 44

SP - 921

EP - 928

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

IS - 11

ER -