On the difference equation Xn+1=α+Xpn/Xpn−1

Abstract

We study, firstly, the dynamics of the difference equation Xn+1=α+Xpn/Xpn−1, with p∈(0,1) and α∈[0,∞). Then, we generalize our results to the (k+ 1)th order difference equation Xn+1=α+Xpn/pn−k, k=2,3,... with positive initial conditions