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 |
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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 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematics(all)
- Physics and Astronomy(all)
- Applied Mathematics