Counterexample of Perron in the Discrete Case

Extended material G.A. Leonov, N.V. Kuznetsov, Time-Varying Linearization and the Perron effects, International Journal of Bifurcation and Chaos, Vol. 17, No. 4, 2007, pp. 1079-1107 Kuznetsov N.V., Leonov G.A., On stability by the first approximation for discrete systems, 2005 International Conference on Physics and Control, PhysCon 2005, Proceedings Volume 2005, 2005, art. num. 1514053, pp. 596-599 Izv. RAEN, Diff. Uravn., No5, 2001, pp. 71