A new characterization of periodic oscillations in periodic difference equations - Al-Salman, Ahmad (2011)
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.