#### Document Type

Post-Print

#### Publication Date

7-2003

#### Abstract

Autonomous difference equations of the form *x*_{n+1} = ƒ (*x _{n}*) 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

*x*

_{n+1}= ƒ (

*x*),

_{n}*n*∈ Ζ

^{+}. Our main focus in this note will be on periodic difference equations in which the sequence ƒ

_{n}is periodic. Most of the open problems and conjectures in this part are motivated by recent work by Elaydi and Sacker [3], Elaydi and Yakubu [4] [5], and Elaydi [2]. 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 [7]) 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 [8].

#### Editor

Saber Elaydi, Gerry Ladas, Jianhong Wu, & Xingfu Zou

#### Publisher

American Mathematical Society

#### City

Providence

#### ISBN

9780821833544

#### Repository Citation

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.

#### Publication Information

Fields Institute Communications: Difference and Differential Equations