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 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.
| Original language | English |
|---|---|
| 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
A new characterization of periodic oscillations in periodic difference equations. / Al-Salman, Ahmad; Alsharawi, Ziyad.
In: Chaos, Solitons and Fractals, Vol. 44, No. 11, 11.2011, p. 921-928.Research output: Contribution to journal › Article
}
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
AN - SCOPUS:80054042435
VL - 44
SP - 921
EP - 928
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
SN - 0960-0779
IS - 11
ER -