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Abstract
Some results obtained with the renormalization group decimation technique recently applied to some particular cases are discussed in the context of the tight-binding model for a one-dimensional chain with nearest-neighbour interactions, Ordered. with one impurity: incommensurate and with completely random diagonal ‘energy’ parameters; ordered with longer range interactions; ordered twodimensional lattice; and pure fractal (Sierpinski gasket) structures are considered. Emphasis is laid on the behaviour of the parameters upon the iteration from which localization properties are obtained. A short discussion of recent approaches for the calculation of densities of states in one dimension is also presented.