Asymptotic behavior of solutions of Poincaré recurrence systems (Q1334606)

Sufficient conditions are given for the Poincaré recurrence system \(y(m + 1) = (A + P(m))y(m)\) to have a solution \(\widehat y(m) = \lambda_ r^ m [v^{(r)} + O (\alpha^{-m} \Phi (m))]\) where \(\lambda_ r\) \((r = 1, \dots, n)\) are the eigenvalues of the matrix \(A\) and \(v^{(r)}\) are the corresponding eigenvectors.