Jun Li - Asymptotic behavior of a linear vector recurrence

We describe the asymptotic behavior of some linear vector recurrences of the form v_n=Av_n-1+b. This behavior depends mainly on the dominant Jordan matrice associated with A. The analysis will be done by dealing with two particular cases: 1 is not an eigenvalue of Aand 1 is the only eigenvalue of A. In the general case, the asymptotic behavior will be obtained by decomposing the vector space into the direct sum of two invariant vector subspaces.