Asymptotic expansions for higher-order scalar difference equations (Q2472245)

An asymptotic expansion of the solutions of higher-order Poincaré difference equation in terms of the characteristic solutions of the limiting equation is given. As a consequence, an asymptotic description of the solutions approaching a hyperbolic equilibrium of a higher-order nonlinear difference equation with sufficiently smooth nonlinearity is obtained. The proof is based on the inversion formula for the Z-transform and the residue theorem. An application for a second-order rational difference equation is presented.