# Solutions of 2-dim Difference Equations

Kyriakos Kefalas

Closed form solutions of 2-dim systems of autonomous difference equations.

In this article we consider closed form solutions of 2-dim systems of autonomous difference equations (DfE). We do not present solutions which are directly available with the RSolve command of Mathematica.

In the following, u, and v, are the unknown functions, the function S, is the successor function ( S(x) = x+1 ) and a, b, c, …r, s,…, are arbitrary parameters defined for each solution.

${\color{Blue}&space;\begin{pmatrix}&space;u\circ&space;S=u^{2}-v^{2}\\&space;v\circ&space;S=2u&space;v&space;\end{pmatrix}}$

In construction.