Autonomous difference equations of the form xn+1 = ƒ (xn) may model populations of species with nonoverlaping generations such as fish, orchard pests, etc. The drawback of such models is that they do not account for environmental fluctuations or seasonal changes. Hence we are led to nonautonomous difference equations of the form xn+1 = ƒ (xn), n ∈ Ζ+. Our main focus in this note will be on periodic difference equations in which the sequence ƒn is periodic. Most of the open problems and conjectures in this part are motivated by recent work by Elaydi and Sacker , Elaydi and Yakubu  , and Elaydi . The second part of the paper discussed the connection between a nonautonomous difference equation and its limiting equation. We present here several conjectures and open problems pertaining to the properties of omega limited sets (see Kempf ) and the question of lifting properties from the limiting equation to the original equation. For the convenience of the reader we introduce in Section 4 some rudiments of the theory of skew-product dynamical systems .
Saber Elaydi, Gerry Ladas, Jianhong Wu, & Xingfu Zou
American Mathematical Society
Elaydi, S. (2004). Nonautonomous difference equations: Open problems and conjectures. In S. Elaydi, G. Ladas, J. Wu, & X. Zou (Eds.), Fields Institute Communications: Difference and Differential Equations (423-428). Providence, RI: American Mathematical Society.
Fields Institute Communications: Difference and Differential Equations