Periodicities of a System of Difference Equations. (24th December 2017) - Quan, Weizhen; Pan, Miaoqiao; Li, Xiaopei
Abstract : We study the periodicities of a system of difference equations x n + 1 = m a x 1 / x n, A n / y n - k, y n + 1 = m a x 1 / y n, B n / x n - k, where initial values ( x - k, y - k ), …, ( x 0, y 0 ) ∈ ( 0, + ∞ ) × ( 0, + ∞ ) . We show that if A n, B n ∈ ( 0, 1 ) are two periodic sequences, then every solution of the above system is eventually periodic with period 2. If k is even, there must be one in x n and y n converges to period two solution.