  The goal of this paper is two-fold. First, based on the interpretation of a
quantum tight-binding model in terms of a classical Hamiltonian map, we
consider the Anderson localization (AL) problem as the Fermi-Pasta-Ulam (FPU)
effect in a modified dynamical system containing both stable and unstable
(inverted) modes. Delocalized states in the AL are analogous to the stable
quasi-periodic motion in FPU; whereas localized states are analogous to
thermalization, respectively. The second aim is to use the classical Hamilton
map for a simplified derivation of \textit{exact} equations for the
localization operator $H(z)$. The letter was presented earlier [J.Phys.:
Condens. Matter {\bf 14} (2002) 13777] treating the AL as a generalized
diffusion in a dynamical system. We demonstrate that counter-intuitive results
of our studies of the AL are similar to the FPU counter-intuitivity.
