Department of Mathematics & Computer Science,

University of Wisconsin--Whitewater,

Whitewater, Wisconsin, 53190 USA

E-mail: arriolal@uww.edu

and

Theoretical Division,

Group T7: Mathematical Modeling & Analysis,

Los Alamos National Laboratory,

Los Alamos, NM USA

E-mail: arriola@t7.lanl.gov

**Invariants/symmetries for autonomous difference equations**

**Abstract:**

Given an autonomous ordinary difference equation, a global first integral/invariant
is a function which remains invariant on the forward orbit of the difference
equation. Furthermore, these invariants are a special form of Lie group
symmetries. We discuss some of the geometric implications and present a
functional equation, which if solved, would give an invariant.