| Contents |
| Consider second order difference equation $x_{n+2}=f(x_{n},x_{n+1})$. An invariant is a non-constant function $I(x,y)$ such that $I(x_n,x_{n+1})=I(x_{n+1},x_{n+2})$. It is clear that it is equivalent to have invariants for a difference equation that to have first integrals for its associated discrete dynamical system $F(x,y)=(y,f(x,y))$. Similar concepts can also be introduced for higher order or for non-autonomous difference equations. In this talk we will introduce several results about the existence or non-existence of first integrals of discrete dynamical systems. We will apply them to several know difference equations. |
|