A new characterization of periodic oscillations in periodic difference equations
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...
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| Format: | article |
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2011
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| Online Access: | http://hdl.handle.net/11073/16694 |
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| Summary: | 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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