Department of Mathematics & Computer Science,
University of Wisconsin--Whitewater,
Whitewater, Wisconsin, 53190 USA
E-mail: arriolal@uww.edu
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

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.