A new characterization of periodic oscillations in periodic difference equations |
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Authors: | Ahmad Al-Salman Ziyad AlSharawi |
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Affiliation: | Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, PC 123, Al-Khod, Oman |
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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. |
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